I was thinking more along the lines of "get 100 credits in this game by giving us your gmail password/control over outlook so we can send to people in your contacts list" rather than outright blind spamming.
I imagine that GMail, Yahoo, AOL, and all of the major email providers would slam that door shut pretty quickly. Much faster than Facebook closed the door on inter-friend spam.
After all, a webmail provider gets nothing from such behavior, and it represent a giant security liability.
One could wish. I'm still getting spam from linkedin and couple of others "social networks" (badoo and similars) even after reporting every email from them as spam.