I don't have a pop door, I have the door I use. If any preditor wants chicken for dinner , it will not have a problem with free ranging birds.
I do not have room for a door, yet the pen I have takes in the whole front of the yard and I walk through one gate and up to the hen house door.
If I want to let them out into the garden etc free ranging, I open the gate and they come and go as they please.
The only problem with free ranging is that you have no control where they go. Mine ended up at the neighbors, through the woods, acrossed the bog and what a pain in the butt it was keeping track of them! So we put up 3' fence, the cheap plastic stuff you can get at wallmart and fenced in 1/2 acre plot for them. They keep content! Good luck, no you do not need a door.