You can copy your Thunderbird profile to the NAS and have Thunderbird pick
it up from a network share, but I think Thunderbird will only allow one
client to use a profile at a time. So you could do it, but you'd have to
close TB on one machine before opening on another.
Also, things get awkward if the versions of TB on each machine are
different, so you'd need to upgrade both at the same time.
Theo