Can bad gas cause fuel injectors to fail?

Based on this information, I doubt that the problem is fuel injectors, but yes, poor fuel can gunk up fuel injectors, and the injectors used by GM in those days were fairly sensitive to fuel quality. I am not familiar with your particular engine, but generally, removing fuel injectors is only a little more work work than removing spark plugs.

If the problem is fuel injectors, adding different fuel or pouring fuel injector cleaner (e.g. Techron) into the tank is not going to help at this point. Some mechanics pull them out and others pump cleaner through them in place, but the best approach is to take them to someone who will ultrasonically clean them and check the flow and spray pattern. Witchhunter and Cruzin Performance do this via mail order in about a week if no one locally does it. I doubt that new injectors are called for, though that is the quickest and most profitable course of action for your mechanic.