Nailing my colours to the mast on this one, I'd argue that in all but the most egregious cases the answer is no, largely because some of the science SE sites kick those questions over to us in the first place because they don't see them as worthy of their time, but I also think there's a deeper and more subtle reason that needs to be considered here in light of recent events.
Unless you've been living under a rock or (like me) have been on holiday to somewhere without the internet for a couple of weeks, you will have noticed all the goings on regarding the dismissal of Monica as a moderator and the fallout that has ensued. First of all, a big call out to Monica; your passion on the sites has not gone unnoticed even by those of us who have been silent until now on the matter and I for one have always greatly appreciated your work on this and several other sites in that you were a voice of reason at times when it was most needed. Words like 'thank you for your service' don't even begin to cover it. But, back to the matter at hand.
We have moderators quitting, others on go-slows or at least not being as active at policing the site as they have been in the past, and now with JBH (and I'm sure others) who are NOT moderators but have been active contributors to both the content and policing of the site leaving or going inactive, now is not the time to get super strict about the questions that are brought to bear on this site in my humble opinion. Why? Because closure, negative comments, downvoting and other strategies we have to manage a question and make it better are perceived by outsiders as confrontational and unwelcoming and it takes a great deal of finesse and personal interaction with new users to make people understand what we're doing and why. We're down on numbers at the moment and the number of questions being posted also seems to be down, and for some of us the fun is in answering questions that we like to provide answers to, not in making sure that the questions fit a narrow brief in the first place.
I've been on this site for 2 years now, and I see new blood rising through the ranks, trying to keep questions on point and assist people newer than themselves understand what we're trying to do here and therefore how to frame a question to make it a good fit for the site, etc. I'll openly admit I don't do that, because I'm not here to make stack exchange a great website; I'm here to have fun answering questions. If a question comes up that I can answer and I want to answer, I tend to answer it. If it's not properly formed but I understand what they're trying to get at, I'll also answer it. That has sometimes got me into trouble but like I say, I'm not here to make SE great.
I'm not going to stand for any new moderator elections, and I have no interest in policing the site beyond that needed to ensure that good questions keep rolling in. Others will disagree with my position, and they're welcome to do so of course, but it's as simple as me knowing why I'm here and what I want out of the site.
I'd also add one more perspective; focusing on the big rules rather than trying to enforce all the smaller ones as well is not only more viable with our current situation on the site, but will also give us the reputation for being a little more welcoming. This strict adherence to the letter of the law makes us appear from the outside as xenophobic and I once even read a post that said 'there are Harvard Alumni forums that are more welcoming than Stack Exchange'. Ouch. Perhaps the one piece of good that can come from all that has happened these past few weeks is that we can go some way to changing that kind of opinion by being a little more flexible with some of the less important rules.
I'd also like to say one final thing in closing; while I applaud the tireless work of moderators and senior contributors to this site to make it a great site for the kind of questions we answer, recent events seem to indicate that we do so under a false presumption. SE has always said that it is OUR site, run by the community and for the community. If that was really true, then Monica would still be a Moderator. SE is run by SE, for SE, and we're - in a word - collaborators to that cause. We've been sucking down the kool-ade, and now we have a better idea what they've been putting in it.
Where do I go from here? Honestly I don't know. If a good question comes up I may answer it but I'm firmly of the opinion that if SE want this level of control over the site, then they should carry more of the responsibility for the quality of the site, not push that back down to us. No taxation (of our time) without representation, and all that.
So, no. I'm in no hurry to create a rod for our own backs and generate a massive amount of work for ourselves at a time when moderation is needed for other higher priority situations by policing some of the less important rules. But, I'm thankful the question got asked so I could put in my $0.02