Gearing comes into play mostly for ensuring the engine is at (or closer to) its sweet spot in terms of powerband. That's why higher gears (lower # numerically) are great for fuel economy (where the goal is to get to the highest gear, spinning the least RPM to do so).
You won't damage your 3.42 doing recovery for friends (especially if you're not doing it all day, every day) but you might have to rev the motor a little higher to put enough power down to pull out the stuck vehicle (and / or engage 4Low)
Really, for that purpose, it's not going to be that much difference between 3.42 and 3.73 (which would've been the only other gear you could've gotten w/ the 5.3L - and maybe not by the time your 2006 came along - I'd have to check). It's so little of a difference that it'd be a waste to find / install used diffs (you need both f/r, with 4WD) or find someone to install new 3.73s in your existing diff (assuming they'd fit in your rear carrier, especially). So keep what you got, especially if you have the locking rear diff ('G80' on the label in your glovebox (edit: see below). If you *don't* have the locker, maybe you *do* want to consider a diff / gear swap from another TB / Envoy.
Depending on how often you get called to do recovery, a winch might be a good idea (along with all of the other stuff that goes with that). With one of those, you can even potentially get yourself out of a ditch.
If you're interested in off-road and all that entails (including winching, recovery, swapping gears, etc.) -- hop on over to Offroadtb.com . Good stuff there - one of our own (no longer here, but we don't call him a 'former' member) had a hand in getting that site off the ground. Pirate4x4 is another good site for gears (but they're not GM-specific)
And as Moose mentioned while I was writing this up -- get the AFM disabled or removed. I'd be worried more about that causing damage, than your gearing, tbh.
*** on edit: You may have 'G86' instead of 'G80'. Which is still good - it's a limited slip. My Sierra has the G80 (Eaton), and I think the 360s / 370s got the G86 LSD