And promptly moved back out, and into the calibre subforums

since the question is about a calibre feature, used in tandem with a Kindle but which technically could involve calibre and anything-else-not-a-Kindle.
(Well, to be fair I guess it could go with calibre or Kindles, but I think it goes better with calibre. Definitely not the Library though

)
And in answer to the OP's question:
Yes, you can use Gmail, or indeed any email provider at all, IF you manually fill in the server information rather than using the two (2) available presets.
Do note that there are a couple annoying things about Gmail, specifically the note here:
http://manual.calibre-ebook.com/faq....-using-calibre
The correct server information for Gmail is the hostname "smtp.gmail.com", with the port # "587" and your
full email username (include the @gmail.com bit)