Having finally summoned up the courage to attempt to install CrossOver 3 Pro manually rather than using the Xandros Networks installer (the Loki installer version worked perfectly for me!) I'm able to try it now with The Bat! v2.12.0.
Earlier problems with resizing columns in the Account Tree pane (and in the new Virtual Folders and Unread Folders panes), and in the Dispatcher all remain. The headers can be resized but the columns below them stay the original size so the headers don't line up with the column contents.
The Quick Search function won't work properly - I can only type one letter which then vanishes and I type another and that vanishes, and so on. Pretty useless really!
The annoyance of the TB! window minimising every time I move between desktops has gone... it now stays as it should do, so that's a plus.
The new TB! features of smilies and images (known as Roguemoticons) work fine.
I'm still playing with TB! under CO3 to see what else works and doesn't.