Will dishwasher drain if sink doesn't drain and garbage disposal is rusted in place.

Depends on your setup. Most often, the DW empties into the upper portion of the GD and no, it will not drain.

I've have also seen where the DW drains directly into the drain pipe after the disposal, then yes, it will drain. Go look where the hose goes.

I guess it is the upper portion. (It is if you divide the height by two, and it is above the place where the case bolts together.)

Is there a way to clean out the disposal enough to make the water drain, without running the disposal.

I guess, since I have to replace the disposal, I would even use something as strong as dran-o, but otoh, if it doesn't work, then I would have to remove the disposal with something like Drano in it.

Is there something strong enough to free up easy stuff that is soaking wet but which won't damage me if it doesn't work?

I never actively put food or any non liquid down the disposal, but it clogs every few months anyhow, I and I have to run it to make the water drain well. The only thing I know is down there is milk curds and 4 to 8 oz. of grease that this one time only I spilled into the sink.

Well, I know it doesn't do that.