Yes, that's certainly possible, but you will have to check which capturing groups matched:
/^(?:(\d\d)-([a-z]{3})-(\d{4})|([a-z]{3})-(\d\d)-(\d{4}))$/i
If groups 1 through 3 are defined after the match, then dd-MMM-yyyy was used, if groups 4 through 6 are defined, then the other was used.
This regex doesn't do any plausibility checking, so it would match 99-XXX-9999 as well, but that's a different problem.
