For anyone with a European passport, short answer is no.
The RFL has tried with the non-federation trained player thing, the clubs agreed to it and almost instantly it was legally challenged by a player (or 2) so has limited powers and the boundaries pushed by the clubs.
The RFL want a limit but unless the clubs 100% go along with it, I doubt it will be any use.
The RFL could do something about it if they wished, without infringing employment law.
Firstly, all applications for visas and work permits have to be endorsed by the governing body before the Home Office will consider them. So the RFL could, if they wished, refuse to endorse as many applications as they currently do.
Secondly, while clubs are free to employ as many overseas players as they wish, the RFL could include something in the rules of the competition restricting the number who may play at any one time. There are no employment issues in that players are not suffering restraint of trade due to being employed. They may have a right to employment but they don't have a right to play.