I'm not even sure it's technically possible but I can ask the CMs.
Personally, I don't really think we need this. The moderators get an auto flag when a question hits 10 answers or 20 comments on the same post but I've been reluctant to protect questions too much. If you feel that a question is getting a lot of bad attention, please flag it, like Zizouz212 says.
My concern, and why I've been reluctant to protect questions, is that much of the content that we've gotten from new users has been great. Not every post is bad and while we prevent bad posts, we also prevent great ones and we limit the number of users who join the site and start participating. We need to be cognizant of this and find a balance. This is why the auto protect requires three deleted answers... if the answers are bad and get deleted, then the protection makes sense (and the auto protection will kick in after three are deleted). If the answers are good, then we shouldn't protect the post.
Part of the problem is that we need our active users to be more active at flagging, commenting, and downvoting low-quality posts. And (though unrelated to answers) voting to close questions lacking in detail. Auto protection is great but it's also a bit of a crutch. We want to be active users, not rely on the system to do the work for us.
So, please flag answers you feel don't meet our minimum guidelines so that they go into the queue. Also remember that voting (downvoting) is important as is commenting. I also think we should start using post notices more to encourage users to add detail or sources, depending on the answer. I've been doing this a bit today with some reasonable success but we should probably discuss it more before we overuse it.
I haven't had any "can you please protect this question flags" and I don't think that any non-automatic flags have taken more than a day to be handled here since the mods were appointed. Before then we were dependent on the CMs for their time and attention, so it's not much of a judge of flag handling time.