I'd be careful with that. Most people probably wouldn't try too hard to promote you, and "just tweeting so I can use this crappy inbox cleaner. bit.ly/asdf..." isn't really great promotion.

In general forcing viral activity both misses the point and fails to work. I'd say you should at most randomly give away free inbox cleanings to your followers / people who tweet about the service. Really, though, you should probably just be active on twitter and talk to people. That doesn't scale well, but it's the most effective viral tactic there is.