In OOTP-18, you can't directly use teams in the tournament. You can kind of cheat by setting up a tournament that draws players from "affiliated" teams, and then set the affiliations so that there's only one affiliation. But they'll be separate teams, with separate histories and all, and may not draw everything in the same way (for example, they'll use different strategies, have different managers, etc...)
Luckily, in OOTP19, you'll be able to do exactly what you want

So if you can wait 2 weeks, you can set this up pretty easily.