She's your boat, you can and should keep sailing, to do exactly what you mentioned, check repairs aka "Leak Test" or "Float Test." She's already passed "Sea Trials" and you are having fun tinkering with her.
If you happen to find more water inside the hull after a sail, just sponge it out. Depending on the amount, it may or may not be worth investigating where the leak is. Boats will only get messed up when their owners leave water inside the hull for extended periods, months or years, as even "closed cell" foam will absorb water if left submerged for months. Yours is not in that category.
Can't I just plug that in when the boat is not on the water, and otherwise continue to sail it normally? Yes
Or does even having it out on the water somehow re-dampen the interior and undercut the drying process, even without an actual liquid-water leak? Most boats make water, unless you live in Arizona. A very small amount of moisture suspended in air could be condensed from the air as a warm hull cools, but that small amount of water will evaporate back into the air with heat vs soaking into the foam.