Yes. I bet it would. I've seen all sorts of stuff happen. Engines get scrambled. A weak battery is bad but a dead one seems to be a killer.
What version of PS2 is it? 5 volt or 3 volt.
Having so many MTH engines I have spares on hand to swap out for troubleshooting. Yet I still have to work out what's actually wrong. I only run some of my G scale in the summer and my 2 rail mainly in the winter. Some engines don't even get used in a season. It keeps me on my toes.