Better to take it apart if you can, but no problems cleaning in a water (and acid) solution as long as you can dry it before the water dries inside. You might go from the first bath to a hot water only rinse and then finally an alcohol dunk to chase off the water. Otherwise a hot rinse then blow out as much air as possible and immediately oil the hidden recesses.

By the way, I've done plenty of vintage watch cleaning in the past and water based cleaners are fine as long as you dry the parts throughly.

Brass wire brush or brass Dremel brush is good for those fine rust pits.

David S.