Nope. Get that battery out of there, (unless it's less than about two years old), and put in a new one.
Due to their design, 1987 and newer GM generators develop a real lot of huge voltage spikes. Those spikes can destroy the generator's internal diodes and voltage regulator, and interfere with computer sensor signals. The battery is the key component in damping and absorbing those spikes. They lose their ability to do that as the lead flakes off the plates from age.
Failure to replace the battery at the same time a defective generator is replaced is the cause of repeat generator failures. It's not uncommon to go through four to six replacement generators in the life of the vehicle. Your description of the symptoms suggests the generator may already have a bad diode or voltage regulator.
First of all, if you're taking these measurements from the dash gauge, those are never accurate on any brand of vehicle. The best they are good for is for YOU to notice when something is not normal. You can do the first part of testing the charging system with an inexpensive digital voltmeter. The battery voltage with the engine running must stay between 13.75 and 14.75 volts.
For the second part of the test, you need a professional load tester to measure full-load current output and "ripple voltage". With one bad diode of the six, all you'll be able to get is exactly one third of the generator's maximum rated current. 30 amps from the common 90 amp generator is not enough to run the entire electrical system under all conditions. The battery will have to make up the difference until it slowly runs down.
If the cause of the low voltage is the voltage regulator, ripple voltage will not be excessive. If a diode is defective, ripple voltage will be very high due to the drop in voltage from the one missing phase of the three-phase output.
Saturday, January 24th, 2015 AT 6:53 PM