Hello, and welcome to ECF. Rice doesn't really draw moisture out of circuit boards, unless it's being in direct contact. Better solution would be to get silica-based cat litter from a pet store, which is hygroscopic, and draws water out of the air. You could also buy silica gel directly from the net for cheap, or just get moisture removers and dismantle the "bricks" used in them. If it works, then hooray. If not, there are tons of sites to get similar batteries really cheaply.
As far as breaking the heating element, I don't think so, but it might've trapped washing detergent, which is quite harmful as-is, nevertheless when vaporized/atomized through the heating element in your e-cig. If it's not a replaceable coil tank, I would just toss it and get a new one just in case.