If it is the alternator that was used on a Tahoe, it sure will work on your truck. Just drive it. Gauges can be off a little, loose belt, failing alternator, bad grounds, some kind of charging system wiring issue or it's just plain normal. Sometimes a "one wire" alternator can be a problem. A/C has always been a large load on motor and battery. The compressor clutch and fan motor pull the amps. Together, could be 30A.
The 2001/5.3 Tahoe has a 105A and a 130A "standard". Pretty good.