It's possible depending on the size pond you are going to be building.
For tops, I would go with glass. Plexi will warp, and fast. If you need to use glass, I would look into framing in some new slide windows and fastening it to the top. (laying them down) Then all you have to do is slide part of the window for feeding etc.
I can tell you know that having an indoor pond really does play a big role with humidity. I have a 1500 gallon indoor tank, and it's a hassle with humidity. I have to have an industrial dehumidifier drain into my basement sump simply because one from walmart/lowes etc wouldn't cut it. I keep koi in this, so it's not even heated.
If the drywall underneath is not treated with Kilz, you risk moisture absorption, as well as molding. But, I think since it's painted it's at least protected a little bit, and should be ok depending on the gallonage.