I generally avoid unnecessary or arbitrary grouping of objects for no particular reason, especially when these objects are intended to form one, integral “part”. If the only reason for grouping objects is to avoid having them stick together while you maneuver them into position to assemble or merge them, take that as a cue that you should be brushing up your skills with the Move tool. There’s no good reason to get things all stuck together if you plan your moves in advance: if you don’t have a particular strategy for a move, i.e., the point where where you grab an object and the target where you’re going to snap it, don’t even bother with the move. Grouping a bunch of geometry only to explode it a few seconds later doesn’t make much sense either.
You know, since this part, a manifold, consists of repetitive geometry, you might consider modeling one tee element and then using an array (of copies) to create the manifold itself. No real point in modeling the intersection between the run and the branch more than once, since that is the most laborious part of the procedure.