I wouldn't. Lots of stuff that can rust with alps boards. If not the switches, the plate.
Show Image
(http://farm5.static.flickr.com/4119/4749328950_37940cf5ff_b.jpg)
You would have to disassemble every switch if you were going to try it as the switches could be full of water for weeks if you didn't.
Dishwashers are only good with cheap crappy rubber domes right? Even then, it can warp the plastic or damage the processor.
It's kind of funny how newspapers and general gossip keeps touting that old "high quality" keyboards can be placed in the dishwasher... yeah... they obviously forgot about metal mechanical switches on TRUE keyboards.
And your disgusting keyboard with insect eggs and rust is absolutely puke-awful. Now, I like keyboards, but I could NEVER work on that, UGH. The seller for that keyboard should have paid you to take it, not vice versa.