They can, as in they might, depending on which place you use.
They will, as in our local WILL always check.
I am sure they do always check, as some others may do , but the point I am making is that they don't have to, and it is most likely as a courtesy, due to that particular garages policy.
In fact I would not be surprised that maybe one tester does the check, and another tester at the same garage on a different day, will not, as he never checks any when he does a test.
It is entirely at testers discretion.
They always remove the wheel cover to get to the spare tyre hanging bracket on the back of the wife's SUV, which I understand IS a point to be tested...
The only check necessary on an externally fitted spare wheel or spare wheel carrier is that "it must not be so insecure that it is likely to fall off".
This can be done by giving it a slight wiggle, in similar fashion to wiggling road wheels to test for play and movement in wheel bearings.
To conduct this test, there is zero need to remove anything, and nothing should ever be removed.
If an inspector (like myself) should ever come along, and see anyone removing anything during a test, then the relevant tester and testing house, will get, at the minimum, a written warning from DVSA, or possibly loose their license, if they have had previous warnings, basically two strikes and you are out.