This already happens at Stack Overflow (see New users required to take a tutorial on how the site works) and it doesn't prevent a truckload of crappy questions being posted on an daily basis.
AFAIK, the reasoning is that Stack Exchange lives of the traffic -and of actual visitors using the sites- and raising the bar or putting obstacles is considered counter-productive.
It's totally subjective, but I'd dare to say that almost nobody RTFM, even tech savvy folks first try to use the tool and check the manual afterwards, when something doesn't work or doesn't make sense. I think the percentage of people that would actually read the basic How to Ask guide before asking would be almost the same as new users who respond promptly and pro-actively to any downvoting or guidance comments.
I've checked that Server Fault and Meta Stack Overflow also don't allow anonymous posting nor asking before reading How to Ask and clicking a checkbox "thanks, I will keep these tips in mind when asking". I don't know if this can be enforced locally or is decided at higher levels. Briefly looking at Ubuntu, WordPress, Superuser and Webmaster shows the same behavior: we can simply click Ask Question and post it Signed up or as Guest:
The title input already has What's your Ubuntu question? Be specific. That didn't prevent the Chemistry question shown by the OP. At the sidebar, a mini How to Ask guide highlighting: Is your question about Ubuntu?. Again, no effect on the avid asker. Does Ubuntu mean anything in Chemistry??
###So, no. I don't think reading How to Ask should be mandatory.
Further evidence. The title input field at Ask Different (Apple) has the following (my emphasis):
What's your Apple hardware or software question? Be specific.
That didn't prevent someone from asking a Microsoft (!) question:
