Yes, they will rest -- the tops will die but the tuber will survive. It will be fine if you leave it in its pot until is starts to grow again.

I guess my question is, can I maintain it as a pretty houseplant without resting the bulbs?

This is an interesting question. I was reading something this week about Caladiums that led me to believe that you can, indeed, grow Caladiums inside as houseplants. You know what? Try it. And if it fails, you can replace the bulb come spring for very little. Sometimes that's the only way we find out the answers to these kinds of questions.