Hotmail, Excite, Yahoo all offer what a spammer considers "throwaway" e-mail addresses.
e.g., they get a freemail account, register with your board, and then spam the hell out of someone.
It needs to have some rate-limiting involved. (e.g., maybe you can only invite X users per month, where X is some value calculated based on the number of posts you yourself have made. Likewise, address firstname.lastname@example.org can only RECEIVE Y invitations, to prevent someone from using you to mailbomb someone.)
It gets very cluttered and confusing, and (from my practical experience) isn't worth the effort, as the recipient almost always considers it spam and deletes it without reading.