Unfortunately, it doesn't look like Newsletter supports that.
On the other hand, the Simplenews module has decent Rules support which may make managing your subscribers easier. As far as I know a user account isn't required to subscribe.
Off the top of my head, here is an example of a rule that might automatically add an email address to a subscription list when a new 'Customer' node is created:
IF
(condition) 'After saving new content' (node is created)
AND
(condition) 'Entity is of type' (node is 'Customer' type)
AND
(condition) 'Entity has field' (node has 'email' field)
THEN
(action) 'Set a data value' (get value of email field)
THEN
(action) 'Subscribe an e-mail address to a newsletter'
(The full implementation is beyond the scope of this answer but there are plenty of other posts dealing with Rules.)
As for importing email addresses, in both of the 7.x branches there is a "mass subscribe" option at People > Subscriptions.