F150 supercab ecoboost comes with three box lengths, according to the Ford F150 website:
5.5' box = 133.3-inch wheelbase;
6.5' box = 144.5-inch wheelbase (12-inch longer box and 11-inch longer wheelbase than the 5.5);
8.0' box = 163.1-inch wheelbase (18-inch longer box and 19-inch longer wheelbase than the 6.5).
Longer box means longer wheelbase, but not a longer distance from the rear axle to the hitch. So, no, an extension hitch doesn't equate to a longer box in terms of vehicle geometry.
Here's a comparison for you: The Airstream Interstate has a rated towing capacity of 7500 pounds. The 2013 Extended version, however, is only 16 inches longer (all behind the rear axle), but has the rated towing capacity reduced to only 5000 pounds, for exactly the same hitch receiver. And this is on a vehicle with a 170-inch wheelbase.
No one can stop you from using an extension if you really want to, but you will lose towing capacity if you do. And you'll need longer safety chains, longer wiring to plug in your trailer, and probably some other modifications to either the trailer or the tow venicle.
I thought getting old would take longer!