Obviously, I would taunt him into attacking me, or use a Frenzy spell on him so I can kill him without being permanently expelled, but will the quest work properly if he's already dead, rendering me unable to give him the letter to become Arch-Mage peacefully, or to challenge him in the arena in Vivec?
Without the use of console commands? You can effectively do anything with console commands. The only way other than that, if you've already killed him, is if you killed him while already being a "Master Wizard" at the actual time you killed him. (The rank in the guild directly preceding Arch-Mage) If you weren't, then no, you can't become Arch-Mage.
If you are not opposed to using Console Commands, the easiest thing to do would be
Find his corpse.
Open console commands (~ key on PC, typically)
Click on his corpse.
Type 'resurrect' without the apostrophes.
Press Enter. He should then be alive again. If he attempts to attack you afterwards, open console commands again, referencing him, and enter 'stopcombat'. Then you can bribe him to like you more, and not attack you.
Hope this helps. :)
If you can't find his body, you can also try:
[resurrect trebonius artorius] (without the brackets)
["trebonius artorius"->resurrect] (with quotes, no brackets though)
If he still wants to kill you when he sees you,
["trebonius artorius"->setfight 0] (with quotes, no brackets)
If you want to see him immediately after entering this, you can use the placeatme command:
[placeatpc "Trebonius" 20,10,1]
If you want to be cheap about it, and skip straight to completing the guild quest and becoming Archmage, you can
[PCRaiseRank "Mages Guild"] in order to gain a rank
[Journal MG_Guildmaster 100] to complete the quest.