No. If for no other reason, I don't think you can win a tournament without shoving in many spots, particularly in late stage play. These shoves are going to technically be 3-bets in many instances.
In theory, I guess it would be possible if the tournament field also had very weak players, but even still it would be highly unlikely to win without 3-betting. At higher skill levels, 3-betting a certain frequency is necessary to not become exploitable.
3-betting is simply one of many "moves" you can choose from and it doesn't make sense to limit your options; 3-betting is very important and you'd need a strong reason to 3-bet less (and not at all is even harder to justify!).
If you consider "sit and go" format as tournament, I would dare to say, maybe, mainly, the 9 and 18 max you could do it, more than 18 players things starts to stay harder, once to reach the top you will need to, often, double your stack.