I'm sure that would be fine but I like to use mineral spirits as it dries without residue. Purple power in a high concentration works well but not quite as fast. Hard to not rely upon a hot pressure washing to ensure anything is flushed, or blasted clean. Given that everything is hot it dries quickly and doesn't really flash rust. Feel and rotate all your bearings to ensure there is no "notching", grit, or erratic feel to them before going back together.
It looks to me that the tractor stripped off a pinion gear and as it was coming apart pieces rode around in the final housing leaving the damage you see in the bull gear and housing. A prior repair possibly replaced just the pinion gear and maybe a couple of catastrophic failure bearings, put it back together and sold the machine as it would now pull itself again. Unscrupulous sellers aplenty at auctions. All these parts work and wear together and I'm thinking if you don't replace everything in there, your good work will be short lived. As pitted and chaffed as that bull gear is, it's mating pinion is going to wear to match till failure. I really think the complete repair is less expensive to do now rather than later.
I know that is an unsolicited opinion but these things get expensive quick to repair and really aren't worth a lot if not operational. It's apart now and should be repaired correctly while in this condition IMO.