Yes, you can do it and in fact it is all about extracting e-mails. Outlook lets you save e-mails to a plain text file so you just need to add a rule to gather all the subscribe messages in a folder and then save them to a text file. You will then need to use eMail Extractor
to extract e-mail addresses.
You can also use a CGI like CGI-Subsribe
that allows you to handle subscriptions from your web site. This script saves the addresses to a plain text file you can use with MaxBulk Mailer. It handles opt-in and opt-out, has an admin panel, sends notifications on new subscribes...etc...
For example click Subscribe
to add yourself to our sample list (just do it, we never use that list, it is only for you to see how it works, you will receive by e-mail a message to confirm your subscription, try also to unsubscribe, and then subscribe again to see what happens in that case).
(Note that it also allows you to send messages, don't use that feature. It is NOT (in general) good for lists of more than, say 100 members, unless you are allowed to run background processes on your web server. If you aren't allowed to do so, and especially, if you don't know what it means by that, don't try to use this with a big list).