Can't see how there could be. Rose wasn't around to do her heart-of-the-TARDIS thing. So, he probably like, exists, but he's not immortal and likely stayed dead on Satellite Five, if he even got as far as travelling with the Doctor at all without Rose there. Which I'm going to assume he did because the Doctor still had to be there to clean up his nanogene mess and oh my head.

There more I think about this alternate Roseless universe, the more it becomes like Torchwood: just don't think about it too hard.