The choice of datum doesn't matter for map making (provided you change datums appropriately, of course). It does matter for transmitting coordinates and sharing data.
To address your last question ("does it even make sense?"), note that UTM is really a coordinate system and as such--in addition to its grid-based zone naming system--it includes a definite datum and unit of measurement as well as a set of projections. What we're talking about here is using its projections (Transverse Mercator (TM) for the low to moderate latitude zones) and its zoning system but possibly changing the datum (and, perhaps, units of measurement). Changing either the datum or the units (or both) is fine, but after that is done the result is not "UTM," strictly speaking. In some applications (e.g., military targeting) it could be dangerously misleading to refer to the resulting (x,y) values as "UTM coordinates," because they will look remarkably like UTM coordinates but might be up to a few hundred meters off. (That can lead to embarrassing things like lost embassies.) Nevertheless, because your principal questions refer to "UTM" in this looser sense, I will also use the term in this way.
UTM is a choice: you can pick any zone to use. It is designed to work within certain accuracy constraints to within 3.5 degrees (longitude) of its meridian at any latitude within the 120 non-polar zones. Because the zones are nominally 6 degrees wide, this allows a 0.5+0.5 = 1 degree longitude overlap with each neighboring zone. Moreover (if you are concerned with map quality foremost and following the UTM system exactly is of lesser importance), the overlap can get larger in the more extreme latitudes (e.g., at 45 degrees the overlap is more than 4 degrees of longitude). Because two (reasonable) datums differ in longitude by at most by 100 meters or so (0.001 degrees), the difference in datum is inconsequential: if you choose a UTM zone based on one datum it will work fine with another.
Once you have allowed yourself the flexibility of changing the datum, you might as well go all the way and create a "custom UTM zone." This is tantamount to dropping UTM altogether (which includes forgetting about the 0.9996 scale factor and origin offsets) and selecting a TM projection suited for the area you are mapping. Within a small area you can do well by placing the meridian of the TM projection through the center of your map and using a scale factor of 1.0000. Choose any convenient origin.
EPSG:3575 is a Lambert Equal-Area Azimuthal projection centered at the North Pole. Although it uses the WGS84 datum, the underlying calculations for this ellipsoid are performed by making a (small) equal-area deformation of the ellipsoid to a sphere (using authalic latitudes) and then applying the spherical projection formulae. Thus, it suffices to understand the spherical form of this projection.
Here is John Snyder's description:
... a point at a given angular distance from the center of the projection is plotted at a distance from the center proportional to the sine of half that angular distance, and at its true azimuth
[p. 185]. For the north polar aspect, the "given angular distance" is just the co-latitude, running from 0 degrees at the North Pole to 90 degrees at the Equator and approaching 180 degrees near the South Pole. As a result, Snyder writes,
The polar aspect ... has circles for parallels of latitude, all centered about the ... Pole, and straight equally spaced radii of these circles for meridians. ... [The] spacing of the parallels gradually decreases with increasing distance from the pole. The opposite pole ... may be shown ... as a large circle surrounding the map, almost half again as far as the Equator from the center. Normally, the projection is not shown beyond one hemisphere (or beyond the Equator in the polar aspect).
[Pp 183-184.]
This image (from mapthematics.com) shows the full Lambert Equal-Area Azimuthal projection in one of its North polar aspects: it is equivalent to rotating EPSG:3575 by 10 degrees counterclockwise. The heavy red line marks the Equator. The outer black circle corresponds to the South Pole.
Snyder's account indicates that although this projection can be used for the entire globe (except for one singular point), it is usually used only for hemispheres. We can easily determine its limits in either case, because of the equal area property. Writing R for the sphere's radius, the total surface area is 4*pi*R^2, whence a hemisphere's area is half that, 2*pi*R^2. Let the corresponding limiting circle (depicting either the Equator or the South Pole) be at a distance r on a 1:1 map. It encloses a region of area pi*r^2, as we well know. Whence
For a full sphere, pi*r^2 = 4*pi*R^2, implying r = 2*R.
For a hemisphere, pi*r^2 = 2*pi*R^2, whence r = sqrt(2)*R.
Since the authalic radius of the WGS84 ellipsoid is 6,371,007.2 meters, either (1) r = 12,742,014.4 meters or (2) r = 9,009,964.8 meters (for the hemisphere only).
In EPSG:3575 the North Pole is centered at (0,0) and there are no false Easting or false Northing coordinates applied. Therefore the extent of the projection is from -r to r in both coordinates. Note that not all coordinates within this extent are valid: the sum of their squares cannot exceed r^2.
In practice, software often (artificially) limits the extent to which it will project or unproject coordinates. Thus, the reason your WMS services did not work as expected may be artificial and software-specific. The only way to determine their true limits is through consulting the documentation (which often is inadequate or nonexistent) or by trial-and-error reverse engineering.
Edit: Eight and One Quarter Percent
Melita Kennedy's (authoritative) response in this same thread indicates that EPSG:3575 is intended for use only in latitudes of 45 degrees or higher. The area of that spherical cap will be (1 - cos(45))/2 = 0.1464466 times the total surface area of the globe. Solving for r as above gives r = 0.7653669*R = 4,876,157.8 m. Thus (regardless of the longitude of origin, which only determines the map orientation) the allowed projected coordinates will lie in the interval [-r, r], just as before, and again the sum of their squares cannot exceed r^2.
The scale errors are proportional to the reciprocal of the cosine of half the colatitude. At (authalic) latitudes less than 45 degrees, half the colatitude exceeds 45/2 degrees. The reciprocal cosine will exceed 1/cos(45/2) = 1.08239... . I thereby interpret the restriction of EPSG:3575 to this limited northerly region as an implicit guarantee that scale distortion will not exceed that factor of roughly eight and one quarter percent. Such guarantees can be useful. However, why this particular factor is important compared to (say) 1.1 or 1.5 or some other finite number seems arbitrary and mysterious.
Reference
Snyder, John. Map Projections--A Working Manual. USGS Professional Paper 1395 (1987). See https://gis.stackexchange.com/a/707 for a cover image and links to free online access.
Best Answer
The bounds are the area that the projection is "well defined" for. The most well known example of a poorly behaved projection is spherical mercator as you move towards the poles (>85 degrees). The projected bounds is this area in the units and projection of the CRS you are interested in while WGS84 bounds are those corners (un)projected in to WGS84.
So I would guess (and with out reading the manual or the code its hard to tell) that the AutoCad developers decided to avoid the risk of mathematical instability or unacceptable errors creeping in and limited you to the safe bounds.