well I'll wade in a here a bit.
IF you have a controlled process and your process variation (Pp & Ppk) is small compared to to your tolerances, THEN the measurement error cannot be very large. Remember that the OBSERVED variation is the square root of the sum of the actual variation and the measurement error, hence a small observed variatoin (relative to the tolerances as stated above) = a small enough measurement error.
As for 2 sources of variation eliminating each other it does happen but not on every measurement: for the observed variation to be small compared to teh tolerances, the measruement error and the actual variation would have to be almost always opposite of each other for the OBSERVED variation to be small....
Now if it were me, there are several different scenarios for performing an MSA. If I had a stabel process and was fairly confident in my ability to detect any negative trending (SPC, etc.) and catastrohic shifts were unlikely AND the severity of the defect escaping was very low OR catastrohic shifts were catchable via some poke yoke device THEN I wouldn't perform an MSA. Otherwise if the severity was high enough and catastrophic shifts were possible I would do the MSA to determine if the gage would detect parts at the spec limit and then I would also most likely guardband.
Certainly I wouldn't put this process on the top of my problem solving priority list if there wre others with worse process performance.
As for teh comment concernign reducing tolerances for very good processes - *I* would think twice about it. If there were evidence that the specs were too loose (field failures that werein spec) I would change them - regardless of the process variation actually. If there were no evidence of 'too loose' specs and their was engineering logic or data supporting their validity then I woudl not change the limits. To me tolerances and processes performance are - and should be - separate things.
There are some who feel that if your performance gets better, you should automatically decrease your tolerance - but if decreasing the tolerance has no value add to the performance (and to the customer - why do it? If we automatically decreased the tolerances on well perfromign processes, we get in the endless loop of having to now improve our Performance to get the desired Ppk - which has tightened up over the years - then we tighten our tolerances then we improve our performance and so on as we fly in ever decreasing concentric circles until we fly up our own...self.