It's possible. We don't really have stats to show the likelihood, though. Have you been tested for hsv1? If you already have it (and depending on your age, most people already have it and most people never get a cold sore), the chances of you getting it in your eye are slim to none as you already have antibodies to protect you from reinfection.
Ask your doctor for a type specific IgG blood test. It can miss some hsv1 infections, but if you are positive, you can put this worry behind you. (Don't let the doctor give you an IgM test - it's terribly unreliable in adults.)
Good luck!