Imagine a question with a certain minimum number of upvotes (10?), with no upvoted or accepted answers. It's a good, answerable question or it wouldn't have the upvotes. Since no one has come up with a good answer, it's a challenge too. I like it. You?
We already have a badge for question upvotes - personally, I think this "extended" badge would only be promoting undesirable behaviour.
Specifically, it would encourage people who ask questions to not upvote or accept any answers until they get the badge. And I'm not sure what additional positive behaviour it would encourage that the upvote badges don't encourage already.
Your heart's in the right place, but I think there's some misunderstanding here about what badges are actually for. Badges are supposed to be incentives to do specific things. Every badge in the current list has a clear purpose, except for Tumbleweed, which is sort of a joke badge and also isn't that far off from what's being proposed here (the only difference is votes). In fact, the only factor that really distinguishes this badge from either Tumbleweed or Nice Question is luck.
So I vote no, sorry. Any badge that doesn't clearly spell out what you're supposed to do in order to get it is ultimately just going to create confusion and negative or unpredictable side-effects. Aside from "ask good questions", which there are already plenty of incentives for, I just can't see what this badge would be trying to promote.