No -- "Eudora 8" is basically Thunderbird,
and uses the same mail storage (and settings, etc.) as Thunderbird;
that's why its use is "completely independent" of any "Classic" Eudora
which may already exist in the same system.
However, "If you install Eudora
it will automatically find and use
your default Thunderbird profile (if it exists)"
Thunderbird (and "Eudora 8") has an "importer" for Eudora
(but not the reverse); any migration between the two
will, in any case, be far from perfect.
However, through the use of either an IMAP account
or "Leave mail on server" for POP, one can use both systems
"simultaneously" to receive the same mail.
One can also "Bcc:" all "sent" mail to oneself,
as a means of sharing even "sent" mail.
A Gmail account (to which all mail for any other account
might be either forwarded or fetched) can also serve
as an alternate POP (or IMAP) server for any email client,
as well as SMTP server, with the web-accessible mail view
serving as a much superior "webmail," permanent storage/backup,
and spam filter -- all currently free, from Google.
"Classic" Eudora (available only for Mac and Windows)
requires a lot of manual conversion, even to "move mailboxes"
(or address books) between these two.
Thunderbird (and "Eudora 8")
should be easier to migrate between different OS;
best to search "mozillazine.org" for info, e.g.:
"Sharing a profile between Windows and Linux"
"Migrate Thunderbird mail (Windows) to Thunderbird Mac OS X"