Yes a plc could do it.
You are talking about a stretch wrap system that will use glue instead of stretch wrap, the kind that puts stretch wrap around pallets etc.
I have used many of the Dynatec glue systems on box forming machines and others. They tend to drip and have to be cleaned up on a regular basis.
What I am not understanding is what exactly are you gluing? Is it the top of the roll or the sides? I am asking to understand the application, most paper facilities just tape and sometimes stretch wrap paper rolls.
I have converted quite a few stretch wrap machines from relays to a PLC. There operation is fairly simple; place the material on the turntable then press start (or an automated conveyor would sense the presence of material and start when in place), the stretch wrap is put in place, the turntable starts rotating, the wrap moves up to cover the necessary height to cover the material then lowers until it reaches bottom, turntable stops rotating after specified number of turns, then wrap is cut and material is removed. The only difference is whether it is a manually loaded or automated system, either way it is not that complicated.
There is always maintenance involved with machinery but the Dynatec glue systems are high maintenance compared to stretch wrap systems overall so I am curious why the need to glue.