Do tweeters with open rear chamber need enclosure?

What tweeter do you mean ? 99% of current design have sealed rear chambers.

Not when used in a dipolar topology as Alon/Nola has been doing for years with VERY good results...

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Even with the open design of the Alon,it is not sharing the same enclosure as the woofer.Open back designs have been around for decades,but I can't think of any that share the same enclosure as the woofer.The Dahlquist DQ10 was an open back design,but both tweeters may have been sealed.The builder of the tweeter,and the midranges would be the one to recommend whether they need an enclosure,or not.I still doubt they would want an open back driver in a shared air(volume) enclosure with the woofer.

What is the speaker in question?

"Not when used in a dipolar topology as Alon/Nola has been doing for years with VERY good results..."

But they still need a baffle or sound waves will cancel.

Even modestly crappy speakers have the woffers, highs, mids in a seperated inclosure.