Charge Controller and Inverter in a Battery Box?

If it's a flooded type battery, I definitely would not, as these batteries emit from time to time corrosive vapors that will get sucked into your electronics and shorten their lives. Venting will release the fumes to the outside, but not before they get circulated around inside the box.

AGM battery don't normally emit gasses / fumes etc, but they are a lot less accepting of improper charging. IF you're sure your charge controller can properly handle and is properly adjusted for AGM, they are maintenance free, no water needs to be added, nor indeed can be added. However, like mentioned, they are relatively easily damaged compared to flooded.
As long as the AGMs are never overcharges, the electronics should be OK in the box - - as long as the inverter and controller do not overhead in the enclosed box. They usually require free airflow for cooling.