I'ts possible, but not easy. The bat angles are different for eveything and sidespin becomes one more added worry on returning chops on the BH. You most likely deal with this on your FH chop by habit.
I did this with some success, but I was easily 2 levels worse. It's far easier to just attack with double inverted than to play defense. In fact, I'd argue that double inverted defense is the hardest style to master. You're basically allowing your enemy to take the initiative most of the time, but without any control rubbers or deception to equal out giving up that initiative.
Youtube has 3 good double inverted choppers, 2 pros and 1 higher level amateur.
Pros:
Satoshi Aida - Defensive Hinoki Blade (Forget the name) and Mark V HPS Max both sides (don't know how he does it)
Nicholay Telnoy - Sword 309 Chop blade with Spinlord Marder 2.0 both sides.
Amateur USATT 2300:
Larry Abass - Defplay Senso with 1.5 Gambler Reflectoid BH, and Vega Pro Max FH.
There are many other vids of Larry and Telnoy, only a few of Aida.