Absolutely...
I remember my French teacher at school had a band, which covered Beatles songs in French, and he was talking about receiving a PRS cheque as they had been played on French radio. I think it was a nice surprise for him, and not his original intention.
I heard that Jarvis Cocker banned radio stations from playing "Disco 2000" just before the millennium - so I suppose that he had some clout in terms of what he could do with his song...
Is it because it would be an administrative nightmare for the PRS to have different requirements for each song? Could you not just donate the money to charity, for example? Or would you like your songs to be free as an incentive to the radio station to play them?