Any Issues, concerns on having a Stored Procedure in Subscriber Database
Subscriber can have different set of objects than publisher. Its perfectly fine to have a stored procedure on subscriber ONLY.

@Tara is correct, it wont drop the proc at the subscriber when you reinitialize the publication.

The only time that I think you would have to remember to recreate the SP is when you have to Initialize a Transactional Subscription from a Backup of publisher .