I answer a lot of questions on Quora. Many of those questions are about automotive things that may be of interest to CarNewsCafe readers. Like this one.
There are a lot of variables to this, so the answer is “sorta.”
Chances are, the battery will give out sooner than later. It could go out with a mere “umph” and stop working (cease taking a charge) or it could go out with a bang and explode. In the former case, you’ll have to get a new battery and figure out what is causing the battery to overcharge (likely the alternator’s voltage regulator). In the latter case, you may have some environmental fees to pay, a lot of repair work to be done on the car (battery acid burns just about everything), and the potential that anyone near to or exposed to the battery was burned by the acid. There could also be an electrical fire started and other issues, in a worst case scenario.
The point is, no matter what happens, that battery being overcharged is not good. Driving the car (running its engine) will keep charging that battery. Making things worse. So get it fixed. ASAP.