That’s possible, I suppose, though JRR said he left his background mysterious on purpose.
The identification with Tulkas doesn’t work for me. Tulkas was a mighty warrior who delighted in feats of strength. If he’d been around on Middle Earth, he’d have wanted to challenge Sauron directly. Given that he’d defeated Melkor, he probably wouldn’t have had any trouble defeating Sauron.
More critically, it seems likely to me that the Valar were put into a different position when Numenor was destroyed near the end of the Second Age.
Their home, Aman, was removed from the circles of the world, and presumably they themselves were isolated from the world. Rather than going themselves to confront Sauron in the Third Age, they sent minions, the five wizards. To me at least this implies Eru had directed them not to interfere directly.
Tulkas was more interested in killing Melkor than anything else, but he could only do that if Melkor was allowed to be released from his eternal prison because he finally repented of his creating crimes against the Valar.
Outside of that, he did like to have a good time. He’s about as close a match, based on the clues in the literature to whom Bombadil could be.