Yes, that's a good idea. Just be sure not to damage the input shaft snout with the drill motor chuck. It might be a good idea to wrap a couple of layers of tape around the end of the shaft, or maybe cut a slice out of a soda can to protect the shaft. It's hardened steel, but being careful is better than having to fix unnecessary damage. Even spinning the box in neutral will splash the solvent around effectively- - - -there's no real reason to engage any forward or reverse gears. Maybe use 4th. gear to get the output shaft and the rear bearing spinning.
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
Love your enemies and drive 'em nuts!