If you mean the rubber keyboard cover, this is really a 'sticky finger proof' cover. It is not designed for full water proofing. If you want to stop things like leaks from affecting it, you should use a bar hood (perspex box custom made to surround the register - often used in wet bar situations).
Yes, you should unplug the register, open it and dry it out as soon as possible. Take the screws out of the bottom of the keyboard and dry the membrane inside the keyboard. Then give it a try.
Registerman
February 2011