Building off that, I'm tending to assume Tom already knew about the Gaunts, since he knew about Slytherin and had found the Chamber and been opening it for a while. I don't think he';ll be able to get back into Hogwarts, certainly not while Dumbledore is still alive, maybe not ever.
It's possible he doesn't make the Diary Horcrux. I don't think he'll be deterred from his desire to be immortal, though. And honestly, given that Dumbledore outright said Tom was probably the most brilliant student Hogwarts ever had, he's probably NEWT-standard in everything by the time of his OWL's as it is.
I could imagine Tom tracks down Morfin Gaunt -- Marvolo would be long dead. If Tom somehow made it out of Hogwarts with his wand -- doubtful, but perhaps if he simply ran and wasn't formally expelled, if he was formally expelled, that's it, wand snapping is part of that. There's no reason for Tom to be impressed with Morfin, and Morfin should recognize Tom's appearance just as he did in canon. what happens next kind of depends on Morfin; if Morfin doesn't bring up that Tom's father is still alive and lives nearby, Tom may never act on that old grudge of his. but i think it's more likely that Morfin does mention it and so Tom overpowers Morfin, takes his wand, and goes off to murder his father and his father's parents. he probably never returns the wand, though, thief that he is. or Morfin's ring. and then that ring becomes the first Horcrux instead of the second.
without even OWL qualifications, or maybe just them, would he get the job at Borgin and Burke's that eventually put him in place to steal Horcruxes three and four (the locket and cup)? who knows. equally, he may never be able to act on the diadem, assuming he'd even charmed the Gray Lady by the end of his fifth year.