I wouldn't bother, personally. If you really needed to improve your osTicket performance, why not upgrade your web hosting package?
If you do decide to run osTicket using nginx, if and when you run into an issue don't forget to try disabling nginx to see if doing so resolves the issue.
(Over in the osTicket Awesome forum I've had users report weird issues that, after spinning my wheels for some time trying to figure out, where eventually resolved by having them switch back to Apache).