Plywood “box” insert between framing 2x4s question

Hi everyone, I’m currently building my woodworking shop, and in the way I had to frame the walls, I have some space between the studs and the cement wall in the back, for the top half of the framing.

It gives me the opportunity of inserting some plywood “boxes” for storage:

[Example of one of the spots](https://i.imgur.com/SmxHvcA.jpg)

In your opinion if I build a box with the front side open, made 1/2 inch plywood, glued and Brad nailed, will that be strong enough to hold over time?

Do I absolutely need to go with 3/4 instead?

Does it need to be screwed in addition to being glued and Brad nailed?

Will screwing the box to the inside of the 2×4 frame secure it well enough?

Appreciate your thoughts!


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