We added https support recently and we tested it on our own Zimbra OSE with self signed certificate so I can say this is working very well.
Our test phone is an Acer Liquid with a cooked ROM under Android 2.1.
Since the minimal requirements for LVContacts are Android 2.x.
The Motorola DEXT is not based on Android 2.x but after some Googling, it seems there's an update of the firmware that has been released few months ago ... since I have no DEXT, I can't confirm anyway.
If you didn't already buy the phone, I would recommend looking at a more recent one since the DEXT is definitely not a bleeding edge model ... If you want to stick to Motorola, you should have a look at the Milestone which have the same features (aka a physical keyboard) but is more powerful, has a better resolution and is based on Android 2.1.