well....at least Thunderbird has (in Account options or prefences, whatever) an option that defines "local directory"..I could imagine this is where the received messages are saved. so the only thing you would have to do is to have both distros share some directory and then set both use that as their local directory...I am not sure about this but as I said, I could imagine this so
so, you could for instance make a small trick so that one of your distros would use some directory, and then in the other distro define that directory to be mounted at boot into some location on your filesystem...
here's an example: let's say you would have a directory called /home/mails/mailbox and that would reside in your hda3 (completely imaginary situation). now you would set your first distro's mailclient to use that directory to save it's mails...then you would open your other distro and do some stuff so it would mount (from hda3) the directory /home/mails/mailbox, and mount it to the filesystem to /home/mails/mailbox that would be in hda4, for example....so the directories would be the same, but only so that the first one would exist in hda3 partition, and the other directory would only be a _mount_ of the otherone, mounted into hda4....that is, if you can't directly use the hda3 location to store mails. and remember, this hda3/hda4/mailbox-stuff was only my imaginary example...
but in a few words: just handle things so you can access some directory in some partition from both distros without problems (ie permissionproblems) and set both clients use that dir.
I haven't done this and all this I wrote is based only on my own thoughts..I can't guarantee it works
probably even won't, but that's the idea I have about this.
good luck...I know what you ask is possible. basically pretty much everything is...it's just to find the way