I'm not a veggie, I wouldn't do well on it at all.
It's possible that there were some traditional groups who were ovo-lacto or ovo-lacto pesce?, but that doesn't seem likely. If you are raising chickens or goats or cows or sheep or whatever for their milk, it seems likely (though not necessarily true) that they also ate the meat of those animals when they were old.
I think it's possible (I don't personally think it's likely, but I could be wrong) some people might do really well/their best on an excellent ovo lacto diet. Definitely not on vegan, I think that veganism quickly depleates your body, and if you don't feel the effects, your children will down the line, and drastically. Humans can't get by without animal protein of some sort (whether meat or eggs or dairy) for an extended period without suffering damage. (For that matter, neither can plants. Either they get meat/manure/feathers/animal products and decaying plants (both, not either or), or they get dinosaur bones, or they run out of nutrients.) I think that if you also ate fish (I realize that isn't true vegetarianism) that most people could do fairly well.
That said, I think that even as a vegetarian (or vegan), you should utilise TF methods of preparation, it will certainly benefit you, even if you might not acheive your highest health potential. Really, who does? TF might take you a step closer, but it won't "get" you "there" I'm not sure there is a there.
For instance, if you don't eat mineral rich bone broths, it's all the more important that you reduce phytic acid, (which depleates minerals), and soaking for 12-24 hours with acid or lemon juice really isn't going to cut it (see the latest wise traditions). Probably a soaking culture for rice, maybe adding a bit of rye sourdough starter (high in phytase, the enzyme which breaks down phytates) to oatmeal as it soaks (which has no phytase, but does have phytates), possibly sprouting and long fermentation of grains would be better. Making mineral rich veggie broths and using them liberally might not be as good as bone broth, but it's certainly important. Choosing small scale, possibly biodynamic farmers, people who feed the soil, to improve the minerals in your veggies, pastured eggs and dairy, so that all of your animal protein has the best possible nutrients.
Eating fermented veggies like sourkrauts will be super helpful to a veggie as well. Etc.
HTH.