If you mean can you use a web-mail address like GMail, HotMail, Outlook &c in Thunderbird then yes.

Thunderbird can't give you a web-mail address, or any other type, as it's an e-mail client not a provider.

If you mean is there @thunderbird.net email addresses that the general public can get then no. There is already a huge number of email providers out there already.

The Thunderbird email client is is operated by the Mozilla Foundation's subsidiary MZLA Technologies Corporation.

Mozilla does manually provide @mozilla.org/.com email addresses to people working for Mozilla in a capacity that warrants having one. If they leave Mozilla then they have to give it up.