Yes it is possible. But not practical ** See Edit 2
Some HTML5 implementations include support for websockets, essentially a tcp connection to a server. Overlay some send/recv code and you can build a SMTP client.
In fact it looks like nodejs and websocket support has been used to implement a smtp client ... see here ...
You would still need a smtp server, username, password, etc just like a standard smtp client in order for it to work.
Using this method for spam would be unlikely as your smtp provider could easily cancel your account.
=== EDIT ===
Actually you could build a server less version, it would have to also implement name server lookups to find mx records. Chances are however that any decent SMTP servers maintain spamlist blacklist tables and connecting from an random ip address would see the email commonly marked as spam.
Also talking to smtp servers that require secure mail connections could be difficult.
As others have mentioned there are malicious uses to this implementation like sending spam. I guess it is possible you could be a HTML5 botnet creator but I would have thought that you would know most of this already :)
=== EDIT 2 ===
As Mark At Ramp51 mentioned, Handshaking is required with websockets. This was something I wasn't aware of. You would have to hack the websocket implementation to bypass handshaking.
The correct way is to have the web server forward the email.