Trying another battery can't hurt (if you don't have to buy one).

But it's unusual for even a bad battery, charged up (14.5 volts) at the start and assuming a good charging system, to lose voltage while the engine has been running. I'm interpreting the O.P.'s initial post to mean that the voltage dropped while the engine was running and supposedly keeping the battery, even a bad one, charged. Usually, a bad battery loses its charge after the engine is shut off (e.g., it can't restart the engine).

And I also interpret his post to mean that this keeps happening. If a battery was really that bad, it might do this one time, but if he can repeat this scenario over and over, that means that the battery charges back up to 14.5 volts each time he tries to repeat this.

But, as your suggested and as I wrote, it can't hurt to try another battery.