What are the consequences of beating Tribunal before Morrowind's main quest?

No, as far as this site explains, the extension assumes that the main quest is complete (or at least progressed far enough). Though it may confuse one if they never started the main quest, it should be ok to do the extension pack before the main quest.

EDIT: Killing the king won't have any negative effect other than losing a reward from him, according to this forum and a wiki excerpt one user included.

Azura has four separate dialogues with the player depending on whether the Main Quest is finished and/or whether Vivec is dead by the time you complete Tribunal, as this page says. And if Vivec is alive by the time you finish Tribunal, he will have some extra dialogue for you after that, as a result of which you will either kill him or will make him permanently disappear into another plane of existence. I assume that if you have yet to finish the Main Quest, then that extra dialogue will only become available after you finish the Main Quest too. But I haven't tried it personally, so I can't say for sure. As for king Helseth, he has no relation to the Main Quest whatsoever, so the order of completion doesn't affect him. You won't get any extra items or anything of the sort.