No, I was concerned that glue might prevent it from lighting correctly. Or, at least, not light up as well as I would like.
Instead, I spent some time working on the “tab”, that is, the part of the acrylic that is hidden inside the fixture. I made sure that it fit snugly and couldn’t wobble from side to side. All three parts have exactly the same tab, so they line up with each other. There are three small screws that hold the fixture closed. I tightened them as tight as I felt was safe, given the fixture is just thin plastic.
There is some small wobble from front to back, but it all stays pretty straight and secure.