Anything is possible really, But I think to answer your question I think you need consider what type of kitchen you are looking for? What type of options are you looking to install?
If you go to install a mini fridge you will require a 110v power outlet, at first glance it appears that you might only have 12v back there. But look around the coach, is there an outlet on a nearby inside wall you might be able to tap into? or perhaps any wiring under the coach?
If you want a Kitchen Sink of sorts you will need to tap into a water line, thankfully with today's PEX parts being so readily available in most home stores you should not have any problems with that. You also might consider the drain in the sink, some larger outside kitchens have a drain hose that dumps into the grey water system, and some I've seen dump into some type of bucket which requires you to dump it
Something else to consider if the sink sounds too much, my little mini kitchen on my rig doesn't have a sink but it does have a little springy hose with a sprayer on the end of it, it's just a quick connect fitting that's near the kitchen and it allows me to hose off dishware when we are done with it outside.
A stove or grill is another matter to consider, if you want those would would have to make a shelf or drawer to put the grill/stove out on, you definitely don't want either of those inside a compartment on your rig. Instead of a drawer You might be able to mount a bracket on the edge of the kitchen space and hang a stove or grill from the side ( like other rigs typically offer).
Some units have propane hookups near the rear of the camper so you can connect a grill into it so you might be able to check for that and leverage it for your kitchen area.
Depending on the depth of the compartment I'm betting your can pull off something basic like this...