Grinding, no. Maybe a whirring sound when the whole 4wd drivetrain is spinning.
Sorry to have to ask, but you aren't running 4WD on dry pavement, correct? You'd be surprised at how many people don't know you can't do that. Doing that will cause your 4WD system to bind up and is really bad for it.
On a new to you vehicle the best bet is to have all the fluids changed out, diffs and transfer case especially since you don't know if/when it was last done. I believe on the GMs it's every 50K miles for servicing. Check which fluids you need, on my 02 Trailblazer it required special fluid in the transfer case which was a dealer only item. Some use regular trans fluid, but check which one you require.
Oh, and use the A4WD sparinging, the auto 4WD spins the whole 4WD drivetrain, the only difference is the front axles aren't engaged at the front differential. Running around all the time in A4WD seems to make things wear out faster (and it'll cost you about 1MPG) on the Trailblazers and I believe the Tahoes/Yukons use the same A4WD setup.