Someone may need to validate this for me but, here goes.
Having a criminal record doesn't necessarily nix your chances, it just limits your options.
Those with DUI's or other criminal driving charges can't operate company vehicles.
Those with theft can't be in situations where they handle money or be in a position where they are responsible for a guests safety.
If you haven't yet applied, pick roles like custodial, housekeeping, entertainment, or character attendant.
Good luck, if you don't get accepted, you may need to wait a year or so, put time in between.