I don't think so. I think it takes 1 kid in the playground to find out about https://distrosea.com/ without understand what a container or VM even is, only discovering that somehow it works, to make us of it.

Then the school admin will block it once there is a peak of traffic through the website, kids will discover proxies, someone will realize there is a business for it, make a free version with ads, etc. It's going to be an arm race and the most dedicated kids, not necessarily the smartest or wisest, will figure it out. Eventually they'll get the concepts behind the tools they mindlessly use until then, eventually find much better tools allowing them to bypass a lot more restrictions.

I don't see how a browser will be able to prevent this kind of usage. They might pass age related information to each page requesting it but it takes a single page to provide the capability without using the information to be enough. If a kid has a computer at home they can setup such a service themselves.