The answer to the original question is yes, and IO540 gives it straight.
Some years ago, when FM immunity was all the 'buzz', but I had not done anything about it, I was flying SVFR, ORTAC to Guernsey on GUR radial (yes, my GPS was on as well).
All normal and calm, needle central, when it suddenly went hard left, no indications of error. Thought 'those French radio stations', and on return spent £?000 getting FM immunity for my Class 1 equip.
Immediately after, attempted an IMCR renewal test, during which we discovered it was generally indicating accurately N-S, but E-W was 15deg wrong! Test aborted.
Umpteen £££ later, was found to be a "sin-cos potentiometer" fault in the indicator. As IO540 says, you get no indication of error.
Yes, I have had twice had GPS go wrong, but never without it being blindingly obvious!
MikeJ