Can “zealot” have a positive connotation?

Zealot, in my experience, is usually used in a negative context, but doesn't have to be.

One quote from the link FumbleFingers quoted in his comment above shows how it can be used in a positive fashion without any apparent controversy:

Your goal should be to transform your satisfied customer into a true zealot for your firm.

And, of course, from someone sharing the same views as the zealot, it can be a good thing indeed:

A true zealot does not do only what is according to the law... he is entirely concerned with the one good thing which is solid, true and eternal.

Zealous and zeal are more often used positively. Again, this is just in my experience. I'm sure there are some for whom the words bring to mind the "zealot".

Zealous representation is characterized by enthusiasm an fervent dedication on the part of the attorney.

He must be zealous in seeking out knowledge.

He had a zeal for learning.

Not for me, it can't: All zealots are "over the top".

But being zealous (that is, having the fervor or ardent desire to do something) can be, in some circumstances, admirable, especially when it involves one's own survival in a hostile environment or helping others survive without regarding the consequences to oneself.

The synonyms for zealous range from mild ("eager") to overweening ("fanatic" and "rabid"). Even passion, which has generally positive connotations, can be overdone and fall into the category of zealotry.

In general, I'd avoid any form of the Z-word if you're trying to praise rather than condemn someone or a group of someones.

Gandhi may have been passionate about a few things, but I wouldn't call him a "zealot". He was committed to a cause, yes, but that alone didn't make him a zealot. Neither was Nelson Mandela, also passionate about a similar cause, a zealot.

You can use zealot positively — you can with a little ingenuity use just about anything just about any way you like, to telling rhetorical effect. But be very very careful, recalling how badly Barry Goldwater’s bold campaign theme (paraphrased by Harry Jaffa from Cicero) backfired:

“I would remind you that extremism in the defense of liberty is no vice! And let me remind you also that moderation in the pursuit of justice is no virtue!”

Zeal and zealous are perhaps less dangerous, but never entirely safe. Think for instance of Ben Jonson's name for one of his obnoxious Puritans, Zeal-of-the-Land Busy.

Starting with the base word, zeal:

The AHDEL gives a definition which is positive if anything (rather than pejorative):

Enthusiastic devotion to a cause, ideal, or goal and tireless diligence in its furtherance.

Collins adds the pejorative flavour:

Fervent or enthusiastic devotion, often extreme or fanatical in nature, as to a religious movement, political cause, ideal, or aspiration.

My own take is that the connotations are positive rather than negative.

Zealous has the same effect on my sensibilities. At least one version of the English Bible contains 'zealous for good works'.

Zealot, however, perversely seems to connote unwarranted fanaticism. Simon was a zealot before his conversion (and a Bible interpreter I know of suggested that that's how two swords could mysteriously appear among the disciples just prior to the Crucifixion).

It's not unknown for closely related words to have very different connotations - contrast:

Thank you for preparing this excellent scheme of work.

I wouldn't trust him - he's a real schemer.