The CDL would lock the transfer case, which is under the gear shifter/coolbox area), but doesn't engage anything in the front wheels. Unless you had an aftermarket front locker engaging the CDL shouldn't lock anything in the front. I wouldn't expect any noise from either side of the vehicle from that. Our front and rear differentials are "open diffs", so when turning power goes to the faster spinning wheel (typically the outer wheel in a turn, unless maybe the inner one is slipping on ice). Using the CDL on dry pavement can cause the center diff inside the transfer case to bind up and basically force one set of wheels to spin/lose (some) traction when they normally have grip.
I think there's a relay for the CDL in the passenger footwell or glovebox area. I haven't checked the wiring diagrams, but whenever I enable my CDL I can tell when it has activated because I can hear a click come from that area. It's possible that relay was clicking trying to activate. Mine is quiet though, not a loud pop or pow just a click, but if you've never used the CDL maybe it's related?
I did once have 4Lo cluck into engagement on dry pavement, so it's possible the actuator for the CDL was sticking/not fully engaging, and when you made the turn the stress caused the actuator to come loose and re-engage until it lined up correctly. I would think the noise would be under the coolbox, but who knows how sound might transmit along the drivetrain?
Personally I'd make sure 4Lo and the CDL engage/disengage correctly a few times the next time you're out on snow (or gravel). If they do then I wouldn't necessarily worry. If you've got some miles on your truck and/or tow with it you might want to flush the transfer case. I do mine every 30k, but I also tow a lot... normal folks could go 100k+