No they won't stay closed until then!
Social distancing in schools is pretty much impossible in the current stay 2m away from everyone sense. Children don't do that, and you can't really expect them to. It would probably be even worse mental health wise - here's your friend right in front of you, but you can't play with them in any normal way?
I'd expect to see primary schools reducing the interactions between classes - staggered breaks and lunches, no assemblies etc to try to reduce spread. Regular cleaning. Low contact pick up arrangements, possibly with staggered start and stop times.
So far there is limited evidence that children are anything like as spready with this coronavirus. Likely because even though they are disgusting little germfests, they don't seem to be nearly as symptomatic which will reduce the number of others they infect.
Older children are a bit easier in some ways (they should actually understand washing hands) but then the constant classroom switching in secondary is an issue.
The aim isn't zero spread though as a PP said, and at an overall population level children and their parents are a lower risk group.