Since this hasn't happened yet...well i don't think so anyway? I'll chuck in my 2c.
It'll have a weird effect of bringing more members in one way but dropping the sign up rate another way.
When i first joined, i needed to sign up if i even wanted to see inside the biology forum, let alone find an answer. It forced me to sign up.
Now i think people will just read at their leisure and not sign up. It already happens before the boards will be made public, check out the userlist of the message board. A lot of the time there are heaps of guests just browsing at their leisure. If allowing access made people sign up there would be less and less guests throughout the year, it always seems to be about the same amount.
Granted some people will sign up to ask but most now that they can read without signing up will do just that.
It's just not about getting members, its about getting members who actually do something on the website. We have heaps of people with 0 posts who signed up just to read or download notes, same situation here.
Also, more than half of the utility/great part of VN for me was the exams. You talk about making education more accessible for the less resourced, exams by far made the biggest impact here. My school gave out maybe 2-3 practice exams. It was a shitty school, i'd imagine the better schools give out more. So many people from disadvantaged schools used VN to level the playing field without paying 100s for exams. Now those people will have to. I know you probably have to do this for legal reasons but still...