Yes, I have an Impressive gelding that was diagnosed with navicular as a 5yo due to improper shoeing. We had to be meticulous about his shoeing but he made a really good horse and was seldom lame. Reining, roping, and some WP. Plus lots of trail riding. When he was younger, my dad would keep him shod with a slightly shorter toe to help with the breakover point and as he got older, we started using a very mild wedge pad. He was finally retired last year at 24 years old. He does have some arthritis along with navicular because he was one of those "horse show babies" that was started at about 1.5 years old. :"( He still runs and plays in the pasture and has always stayed pretty sound. Lots of trail riding on steep hills or uneven terrain did seem to aggravate it but clasymover is right. Navicular is not the end of the road. Good luck with your baby. :)
Ps: I agree with kickshaw. I would avoid the barrels just to keep from making it worse with unneccessary stress on the joints but WP and trail would be fine. Probably would even be good for him. How old is he anyway?