As long as the bottom 2' is plywood (although note that roos will still be able to peek over the top of that to see each other as bedding piles up against it, I have an identical arrangement myself) there is no concern about chicks popping through.
I used 1" chickenwire for the above portion, but unless you have reason to *expect* your roosters to attack each other (remember they often do so aboveground, jumping or flying into a 'kick') I expect 2" would probably be reasonably adequate too. The main disadvantage I would anticipate would be it being less visible so that there is more chance of chcikens temporarily forgetting it's there and trying to fight or fly through it. I have had my large Sussex roo, who is not exactly Mr Graceful, trying to get down from the roost, twice fly into the chickenwire part of the pen divider and get his feet/spurs hung up in it. Once I was there when it happened so could disentangle him immediately; but once I entered the coop a few hours after sunrise and found him hanging upside down there by one leg, which turned out ok but might not have. OTOH it is possible that with 2" mesh there *might* be less tendency to get caught, I dunno. Just reporting.
Good luck, have fun,
Pat
