Yea, Mike Constantino as an example. Just read about him. Also, there is famous one-handed kick-boxer, forgot his name though...

Well, Roy Jones fought Hopkins with one hand almost due to injury and won. One handed people develop extra strengths, so your jabs must be pretty good (potentially). Ali, SRL, SRR, Larry Holmes proved many times that many fights can be won just the the Jab.

If your injured hand allows you to defend properly then why not?