You can't put him in the same category as a Bird, Havlicek or Russell -- those are easy.
Garnett depends on how much of a Celtic you think he is. For his career, he's above Tatum for sure. That's a perennial MVP candidate, top 3-5 All-Time at this position.
McHale is a tough one. I think absolute peak/prime McHale was the bigger force, but it was very brief by comparison. Tatum will beat him on every career number. I think it's ok to put Tatum over him, even if there's a context where you'd pick McHale first for your team.
I'd give him a SLIGHT edge over Pierce, assuming he has another ~3-5 productive years in green. Better peak, 1st team All-NBA level performance. Will still be difficult to catch Pierce on career scoring. Pierce is right there with him in than 2nd tier of career Celts.
Cousy, I think you get into too much of a modern era vs old timey debate to get anywhere useful. Historically, Cousy is probably a bigger deal. Whether you're willing to rank him over modern superstars is up to you.
All told, it seems like the absolute best case scenario for Tatum is around 4th/5th best career Celtic if everything breaks right over the next few years. The floor is several steps lower, below guys like Pierce, McHale, Cousy. Mayyybe below Cowens if things went right off the rails from here?