The question hasn't been answered on TV. Had the 1990 season not been cancelled, the intention was that Ace would leave to go to the Academy on Gallifrey to study to become a Time Lord, so the answer to this question would have been established definitively as "Yes", but the show was cancelled. The question didn't arise in the 1996 TV movie and hasn't been addressed in the revived series.
Even if you turn to the non-TV media, the answer is probably yes, but still not definitely.
The novels dropped some hints about the Doctor's plans to send Ace to Gallifrey, but never directly said what he was planning—and in the end, it never happened, because she went off on her own to be Time's Vigilante instead. One novel implied that Penelope Gate was a Time Lord scientist, even though she was definitely biologically human. A few novels also directly confirmed that non-Time Lord Gallifreyans can become Time Lords, which might imply that non-Time Lords from other planets/species can as well, but that's never mentioned directly.
The audio stories, meanwhile, had the Celestial Intervention Agency deciding that Leela was more useful as a non-Time Lady, implying that either they or Romana could have chosen to make her one if they'd wanted to, but there's no more than that implication.
Some of the novels also implied that some time after the 51st century, humans in general will take over from the Time Lords. And similarly, the standalone webcast Death Comes to Time ended with Ace taking up the mantle of the Time Lords after the fall of Gallifrey (although it's pretty hard to fit that webcast into continuity). But neither of those would count as the Time Lords making humans into Time Lords.
- ↑ Of course in the current universe, the Doctor is the only Time Lord around; if he wanted to start a new Academy, train Amy and Rory, and then declare them Time Lords, it doesn't seem like anyone could really disagree with him. But it also doesn't seem that likely that he'd do such a thing.
- ↑ Or, possibly, that they'll actually go back in time and become the Time Lords of Gallifrey, or that the Gallifreyans of our universe were the humans of the previous one…