Do tweeters with open rear chamber need enclosure?

I would check and see what the tweeter manufacture recommends but separate enclosures have several virtues. That said, every case is different and the ideal isn't always the most practical.

If it doesn't have a sealed back,I would worry about the woofers back pressure causing damage to it.Also, I think the constant pressure changes would move the driver in the tweeter,causing distortion or some sort bad sound results.

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...

~

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.

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

Are you familiar at all with Alon/Nola speakers? Those models that employ the dipolar topology for the midrange and tweeter drivers have the drivers mounted on a baffle.
The Alon line had a seperate baffle of the mid/tweeter driver array mounted on top of the woofer enclosure but the Nola line uses a common baffle.

Do a GIS for Alon/Nola and you'll see what I mean or you can go straight to their website: http://www.nolaspeakers.com/