Yes you can play the tribunal quest any time you like (provided you are tough enough). Also when you've finished the morrowind main quest, the game doesn't end. You can play on as long as you like, so it's not like you have to get it done before you finish morrowind.
I actually installed Tribunal yesterday, after I finished the main quest (because I wanted to go through unpatched if possible) and I would say that it is better to install it sooner rather than later. My journal was chock full of quests and it took a LONG time to parse quests when I loaded my morrowind game - about 40 minutes. So if you install it straight away then you'll bypass all that annoyance. I read two magazines while I waited
