You can do pretty much anything you like, but remember, it will have to pass inspection. If you have anything battery powered on the bot the inspectors will be taking a close look at it.
I would recommend the following, simply from experience.
-Don't carry all of your batteries and chargers on the robot cart, but have a slot for one or two. This will keep the cart light and allow you to charge batteries during matches.
-Use an old FRC battery to run your inverter (to charge the driver's station). Inspectors recognize these batteries and it tends to be easier to convince them of the safety of the setup if things are familiar.
-Make the inverter setup removable, this way if you don't pass inspection you will still be able to use your cart.
-Wire everything like you would your robot, with fuses, a main breaker, etc. You don't need to use the power distribution board to hold your fuses, but have a labeled location for them.
-Lots of common sense, This platform will be a combination of transport, display case and workspace for 3 days. Design with that idea in mind an you will be happy
Good luck, the general design of your cart is up to you guys. Make it unique and fun (while keeping it practical).