It depends on how fast of real-time you are looking at. For example, if you try to make a space battle, and everyone is close, but moving at a high speed, then you may find that the milliseconds difference makes a difference, but, if you are doing something like an auto racing game then it won't make any difference, so TCP is fine.
So, try it, get some numbers and decide if it is acceptable.
The bigger problem will be the difference in bandwidth, so, if one person is playing over a really slow connection, and everyone else are on very fast connections, then that slower player will be a problem. You may need to scale the updates to the slowest connection, and you may find that TCP/UDP issues are not enough of a concern, as the difference in connection speeds are a far bigger problem.
So, test with various connection speeds, with differing numbers of users, each with their own connection speeds, and see if, as one user, the game is still enjoyable.
UPDATE
It is not bandwidth that will be the concern, but the latency, as was pointed out in a comment. I had picked the wrong term, as several people might be able to respond quickly and be closer to real-time, but one user may be much slower, perhaps on a congested network, slow computer, or whatever, but they may only send updates every 1000ms, whereas everyone else is doing it every 100ms.