Like indyfabz said, "It all depends." Clubs are different; some are fast and furious, while others are more relaxed. Some of the larger clubs accommodate both type of riders. It all depends on your ability and aspirations. I ride my cyclocross bike, a Bianchi Volpe, on our club rides without any problems. However, we are more at the relaxed end of the scale. I do have a very light road bike, but it is less fun to ride in the hilly country we have around here. Out of the 3 types of bikes I have, touring, CX, and road; the Bianchi is the one I ride the most.

Bikes like the Tricross and my Bianchi are really generalists. They can do everything from loaded touring to club rides. However, while they can do most things very well, they barely excel in any one thing. Unlike road bikes and dedicated touring bikes, which excel specifically in areas they were designed for, but are not very suitable for riding outside of that range.

I think the Tricross is probably a good all around bike, but you might take a look at the Volpe. Regardless of the bike you choose, get a triple. The triple crank will not slow you down on club rides, and will be nice in the future if you decide to tour.