You can see the proj string used by QGIS to transform from and to WGS84 when you look at
Uusally, all EPSG-codes are bundled with one certain transformation to WGS84 which was decided to be most appropriate. American NAD27 CRS are the only ones which use a ntv2 grid by default instead of three- or seven-parameter Helmert transformation.
If you are unhappy with the accuracy of a defined transformation, you can define a custom CRS with different +towgs84 parameters.
214,1656,4207,4326,"Parameter values from Lisbon to ETRS89 (1) (code
1655). Assumes ETRS89 and WGS 84 can be considered the same to within
the accuracy of the transformation. Replaced by Lisbon to WGS 84 (4)
(code 1988).",For applications to an accuracy of 3
metres.,1294,36.96,42.15,-9.55,-6.19,1,0,9606,
-280.9,-89.8,130.2,-1.721,0.355,-0.371,-5.92,0
215,1944,4207,4326,"Parameter values from Lisbon to ETRS89 (2) (code
1790). Assumes ETRS89 and WGS 84 can be considered the same to within
the accuracy of the transformation.",For applications to an accuracy
of 2 metres.,1294,36.96,42.15,-9.55,-6.19,1,1,9606,
-282.1,-72.2,120,-1.592,0.145,-0.89,-4.46,0
216,1984,4207,4326,,For low resolution
applications.,1294,36.96,42.15,-9.55,-6.19,1,0,9603,
-304.046,-60.576,103.64,,,,,1
217,1988,4207,4326,,For medium resolution
applications.,1294,36.96,42.15,-9.55,-6.19,1,0,9607,
-288.885,-91.744,126.244,1.691,-0.41,0.211,-4.598,0
So you see, that the low resolution transformation with three parameters is used in your example.
It is stored in http://svn.osgeo.org/gdal/trunk/gdal/data/gcs.csv under code 4207 and used by Qgis and other GIS software depending on proj.4.
Best Answer
In QGIS 3.0, on-the-fly (OTF) reprojection is always enabled (https://issues.qgis.org/issues/11644).