Yes you can use regular expressions on column filters but you don't need to in this instance. The column filters are Boolean based so you can just use the expression:
The '<' matches the start of the word, just like '>' matches the end of the word.
However, if you really want to restrict the file to where 'NY' only appears at the start of the file name you can use a regular expression by prefixing it with the operator
Column Filter Example
Narrowing down search results for all songs with the word 'You' in them:
Column Filter with Regular Expression
Using a regular expression we can show just those files that start with the word 'You' after the track number: