Titanium Backup Pro can extract apps or data from a nandroid backup, so I guess you'd want to find the user dictionary in there and restore it.
Now as that's the data for a system app (the HTC keyboard) I cannot guarantee it will be compatible between android versions. You'd probably be OK if you backed up the current one with Titanium, restored from the nandroid using Titanium, then if something was broken restore the current one from the Titanium backup. If you really want to be sure, take another nandroid before doing any of this (you can have more than one).
If you don't have Titanium Pro and don't want to pay, you could do the same in this slightly long-winded way: take a nandroid of your 2.3.3 setup, restore the 2.2.2 nandroid, take a Titanium backup of the user dictionary, restore the 2.3.3 nandroid, then restore the dictionary from the Titanium backup. Then if it works, fine, and if not just restore your 2.3.3 nandroid again.
(There have been a few times when I've flashed a new ROM, realised I'd forgotten to back up something important, so restored the old nandroid in order to make a Titanium backup, then went back to the new ROM and restored the newly backed-up data. It's another reason to always take a nandroid before flashing a new ROM).