It could happen, but herpes infections in the eyes are more likely to happen because of oral herpes infections that travel through nerve groups to the eye.
Herpes in the eye isn't all that common, so try not to worry too much about it. (I know that is easier said than done.)
Has anyone told you about genital hsv1? You can learn a lot about it, like it's less infectious than genital hsv2, in the Herpes Handbook here - https://westoverheights.com/herpes/the-updated-herpes-handbook/ It's free, and written by one of the world's leading experts on herpes.