I have solved an issue with the help of @JoshuaBixby for creating definition queries using REGULAR EXPRESSIONS. I was informed that the LIKE predicate does not work with REGULAR EXPRESSIONS. File geodatabases do support the use of regular expressions and ranges, but with the SIMILAR TO predicate.
I have found no documentation stating this works, but it does. It would be best if the SQL EXPRESSION builder has the option to use SIMILAR TO when building SQL EXPRESSIONS and when writing them out.
