Well, partly. You do not want to overload your JGC, mostly from a safety standpoint. I can appreciate the trailer you want as SWMBO and I own a 2015 White Hawk 20MRB and we love the Murphy bed concept. The trailer feels bigger than 20 foot when the bed is up.
Chances are, you may not ever load your Jeep & Jayco to the max. capacity. In the days of old, it was recommended that if your tow vehicle tow rating was 6000 ponds, it was best to have a 10% leeway, or a trailer weighing about 5400 pounds loaded.
You will have to decide this one, you may buy the 23 MRB and find your JGC does a fine job. A couple of variables here, the brake rotors may be heavy duty. You have an eight speed transmission. Most of us don't have that many gears. You just have to remind yourself to not overload the combo.
2015 White Hawk 20MRB
2011 F150 Non EcoBoost (5.0)