Quite definitely not, I think.
First, I don't think Tom Bombadil was a Vala at all. (Most) Valar are proud and take themselves very important. They were all more or less involved in the war against Morgoth (especially Tulkas) and are definitely very concerned with what happens in Middle-earth. I can't imagine any of them condescending to live like Tom Bombadil, unobtrusive and isolated, dealing only with a few acres of sleepy nature and some Hobbit farmes (Farmer Maggot seems to be one of his favourite regular contacts). Valar prefer feeling important, talking among themselves only and occasionally being worshipped by the lesser or commanding them to do some important mission. Tom, on the other hand, seems hardly (seriously) interested in anything beyond his immediate environment. He doesn't believe in "important missions" (Gandalf, in reply to someone suggesting to give the Ring to Tom to take care of, suspects Tom would forget about it after little time and throw it away).
If he was an Ainu, I would rather assume he was a Maia. Whether due to their larger number, their lesser power or something else, Maiar seem to tend to have a more "local" (less global) perception of the world.
Second, Tulkas was a war god. Tom is the exact opposite of that. He is protective and loving, a (weird) pacifist. I can't imagine Tulkas' preferences change so dramatically: in the First Age (and before), he chose a muscular body, a red skin and had blond hair; and he was not exactly the brightest of the Valar. His favorite hobby is wrestling, he is irascible and rash. None of this is true for Tom. Finally, Tulkas was the last of the Valar to descend to Arda, so if Tom were Tulkas, he would probably not boast himself to be the "eldest and fatherless".
Side note: the eldest of all Ainur was actually Aluin, the lord of Time, but unlike his children (Danuin, day; Ranuin, month; and Fanuin, year), he never descended to Arda.