Being older will not affect you at all-- there have been several "older" people that have gone through my school's program quite successfully, many being in their late twenties, some in their very early thirties.
As long as the arrest was removed from your record and you have NO criminal charges, this will not be used against you.
If you have a decent record from your time in the Navy and have been accepted to a school with ROTC, you can join the program without competing for the scholarship. As long as your grades stay up, your PT looks good, and you're performing within the program, I'd say you have a great chance at being contracted, maybe even offered a scholarship.
Side note: This is not intended to offend anyone, but Gold Bar Recruiters are essentially brand new 2LT's waiting to be sent to their first training... they generally have no expertise in recruiting or specifics on contracting, scholarships, etc. There should be a higher-up who is the scholarship/admissions officer for the program who is the ideal POC for this type of thing. Good luck!!