I have a mare who tore her butt in cut training young. After a few years she went on to be a turn-back & even had a pretty good low-level dressage career.
She was/is always short on that side, even 12yrs later. I used her for low-level reining some (greener than grass, $10NP stuff). She did OK, but wouldn't go down in a slide & her turns/rollbacks on that side were never good. She was always warmed up good, had a chiro, acupuncture/pressure, magnets regular & massaged before & after riding. At a clinic, after she'd been put up & was standing ~1/2 hr, the clinician decided to grab her to use for an example, she'd cooled enough to retear it. She's now a gimped broodmare who can be rode lightly on a good day with bute & a good massage.
My guess, your horse could probably do low-level if you keep up on it and never work him cold, and don't expect to win much.