There is a horse at my barn (13 yr. Old TB mare) that is blind in her left eye, and jumps full courses up to 2'6" at shows. I would say yes- it's very plausible. You may not be the best, but if you can do it at home, you can do it at shows.
Horses with one eye are at a disadvantage however, they can still compete. I have been to tons of NBHA shows and seen people there with one eyed horses. They can tend to be spooky, and you really have to guide them with your legs, weight, and light hands. I personally don't think it would be a good idea to race a completely blind horse. Would you want to run 25 mph with someone on your back and have no clue where you are going? It would be very dangerous. But if you trust the horse enough start slow and work your way up =)
As long as you build a good trusting relationship with her, and start slow so she can get used to what you are asking her to do, I don't know why you can't. Since she's been blind in that eye most of her life, its not a new sudden thing that she has to get used to, and obviously she's learned to cope well enough on her own, so as long as she feels comfortable, I say go for it. John Lyon's horse Zip lost the sight in both of his eyes after an allergic reaction to a drug, and John still used him as his clinic horse, and still went out and worked him over all sorts of stuff. Because the horse trusted the rider, Zip was willing to trust the John wouldn't let him get hurt, or put him in a dangerous situation. Post pictures if you can, I'd love to see your horse.
Yes! I run with a girl that has a horse that lost it's eye. She was already trained for barrels but after losing her eye she would get really nervous..so she went really slow with her and the trick is just gaining alot of trust with the horse and you could do it easily!..Good Luck!