Will it damage a li-poly battery or cause it to swell if you store it in an airtight container such as a large child proof topped pill bottle?

No, it shouldn't. It doesn't need fresh air when it isn't being used. Now, if you seal it when you are pulling energy from it, then you will have a problem.

I wouldn't store them in such a container like that anyway, as they are plastic, and thus not fireproof if something did go wrong with it.

I would use something made of either ceramic, brick or steel or similar to house them in.

I personally use a locked thick-walled steel cash box, kept in the garage with my lipos in it.