There is a mechanism for this, although it's roundabout and definitely doesn't constitute "encouragement" -- it's more like "probation". Users whose question quality is extremely poor, as judged by an automatic filter, will not be allowed to post further questions. One of the ways to regain access is to contribute to the site by posting some quality answers. The obvious
problem difficulty is that this is entirely reactive, not proactive as you are suggesting.
It seems to me that it'd be a fine idea to phase this block in, rather than only revealing it after the user has crossed the threshold. The first n questions, however many the filter needs to start judging, would be "free". If the quality is low, the user could be presented with messages encouraging helping others by posting of answers too. The user could certainly post total crap for answers too, but that doesn't help clear the question block (and there's an answer block, too, essentially the same mechanism as the question block).
As Robert points out, many of the posters of crap questions don't care about anything else but getting help/someone to do their work, but I think it might be worth trying to encourage good behavior, then warn, and then block, rather than suddenly cutting off the ability to ask.
I suspect this is not likely to happen, though. If I recall correctly, Jeff has said that the filter is intended to catch the worst 1% of askers, and I think that he considers them irredeemable.