Supercharger Pulling a Trailer

[CustomCruiser]

First time post, have a quick question.

I drive all across the country in a 04 H2. I pull a 4300 lb trailer for my company, driving from city to city showing off our products.

My company, EATON, is one of the largest suppliers of supercharges in the world.

Question is this: If we add a supercharger, will it help with pulling a trailer? Will it improve gas mileage, and will I still be able to run 87 pump gas.

I appreciate the help.

See attached pic of the Custom Cruiser. My job is to drive around all day in an H2, doesnt get much better than that!