Easily done, except for a few awkward details. Summoned minions are very viable alternatives to having your own character fight, although you'll probably have to assist them with a few spells now and then. There are a couple of situations where repeatedly summoned help simply can't deal with the situation, and only a high-level combat character has a chance (I'm thinking primarily of a particular Bosmer in the expansions). Be aware that summoned minions often spawn behind you, so if you are facing the opponent you will be between your minion and the opponent, directly in the line of fire. Your character may take a few arrows or spell hits before your minions even get into the fight, including shots intended to hit your minions, or even BY your minions at the enemy; turning around or sideways before summoning may help. Worse, you have no control over what spells they cast, or who or what they target. I had one character killed by a series of area-of-effect spells cast by a summoned minion at a cliffracer hovering directly overhead, while the bigger threat approached untouched.
I'd consider the MG well suited for a "mostly good" or morally neutral (only interested in the knowledge) necromancer character, and Telvanni is a viable alternative for practically any magic-oriented character. If you're more into the dark side of things, then either Telvanni or even Morag Tong (working as a magic-based assassin to finance your research) might be the better option.
One character of mine dealt with the MG early on, but gradually shifted his orientation and interests toward Great House Telvanni, advancing in the House while his reputation with the MG steadily deteriorated. He eventually reached the point where several MG members denied him basic services, and several others wouldn't even speak to him, despite not having done anything actually hostile toward the MG. One could also advance in both, and maintain fairly decent relations with both, but advancement in only one will inevitably cause some drop in relations with the other, which would then need to be offset by running missions or raising a whole lot of individual Dispositions.
There are numerous quests all throughout the game which are quite doable by a necromancer, it's just a matter of figuring out how to apply your skills to the situation. Fortunately, most of Morrowind's quests don't demand that you use one particular approach, as long as you accomplish the end result; in fact, many quests reward thinking "outside of the box", where you get additional rewards for not resorting to killing, etc., while others penalize not having done the quest "as ordered", but still consider it "done". Your character should do fine.