No. When they're in the screen they're going to be next to impossible to move. The point of the screen is that you don't have to worry about controlling the canopy using other methods, you just feed the branches through and create an even canopy that way. Taking them in and out of the screen defeats all that canopy control, not to mention risks breaking off branches and, later on in flowering buds themselves.
Try doing a screen like what I'm going to picture for you. I'll show you how they started out, how they were trimmed (canopy control) and how they went. These girls were grown under a single 600W light on a 3' light rail (old rail a friend sent me). The screen used is landscaping barrier stuff, I cut out holes in the screen for better ease of access. If I do another ScrOG I'll use Hortonova trellis instead.
First two pix show the girls how they went in and how they were trimmed up to start. I shave their legs up very high, almost going Brazilian on them. The rest should be self-explanatory.
