A detailed statistical analysis requires more tools than my pay grade allows, so we might end up waiting a bit on that. I thought about some ways to potentially find answers by low-rep users that ended up being quality, but that's kind of a problematic way to slice data and get anything useful out of it. Perhaps one of our SE overlords will grace us with some detailed data, which would probably be definitive.
I did, however, ask around with the mods over on SO to see what their volume is like and how it compares to ours. I found that:
SO started requiring stricter controls to post questions when they reached a daily question volume of ~3-4k. ("Registration required" was their solution) Right now our answer volume hovers between 100-200 per day, which is less than a tenth of what was considered 'critical mass' - requiring a policy change - on SO. (We peak to 4-500 during the early phase of contests, based on my API analysis)
SO mods delete around 10x the amount of content (per mod) that we do. They're electing a few more mods, so presumably they're at their current "moderator event capacity." That's not to say that everything that gets deleted could be prevented by requiring registration, just that it seems like we've got considerable moderator event capacity remaining by SO standards.
From these somewhat rough numbers, I don't really think we have a serious problem with stuff getting posted that requires deletion, unregistered users or not.
In thinking about this question, my mind jumped to something that I think you also thought about (judging by this comment). It's a little bit cart-before-the-horse, but I think it's still relevant given that gathering definitive metrics is likely to be a time consuming process.
What's the tipping-point ratio of bad to good content, that would make it "worth it" to raise the bar for people to post answers?
I think of this somewhat like a spam filter (or other machine learning algorithm) - increasing the bar means probably causing some "false positives" - ie, your credit card bill being marked as spam. How many v14gr4 ads is it worth looking at to ensure that an important message gets through?
As one of the primary filters of such content on the site, I can say I'm honestly not bothered by the volume. The type of clear "not an answer" type stuff you've noted is pretty easy to deal with. Usually there's an auto "low quality" flag or one or two community members have flagged it, and it takes me 2 or 3 clicks to banish it to the great Recycle Bin in the sky. Whether others feel like flagging said content is a bothersome chore is beyond my knowledge, but hopefully they find it just as easy to flag as I do when I handle the flag.
Based just on my personal opinion, I'd rather have fewer barriers and deal with a thousand "not an answer" flags/deletions a month (which is far greater number for me than it is currently) than potentially miss out on even one really worthy answer.