Will I damage my truck?

[Ray-IN]

That 20" is the diameter of the rim, the outside diameter of the tire is not a lot more than a 16" rim's tire.
Shorter sidewalls greatly reduce sidewall sway and heat buildup as a result of sidewall flexation.
Balloon tires were invented back when springs and shocks were not refined enough to improve ride in the vehicle. Now the industry has evolved full-circle and returned to bigger rims and shorter sidewalls, taking advantage of vastly improved suspension designs.
Compare the sidewall height of a 20" tire today with a 16" tire; there isn't a lot of difference in diameter.https://tiresize.com/calculator/

 

[MN Blue Skies]

Thank you all for your responses. Appreciate all the insight. I will not be buying this trailer!

My response along with others is nope. Dear Husband and I have been there and tried that. Our final decision was to buy a used 3500 RAM and not worry about it.

 

[Cybergrunt]

I recently was asking the same question and did my research. Ultimately bought a 3/4T ford with 7.3l gas. Years ago I had a 28' TT I pulled with a 1/2t conversion van. It was doable but swayed every time a truck passed and felt squirrely above 65 mph. Changed to a 3/4t crew cab diesel and had no sway, no need for equalizer hitch, and it felt like I could've gone 80mph with it. that was my lesson on avoiding a marginal tow vehicle.

100%! Currently have a 7.3 F-250 and tow around 55% of capacity - a ton of margin (actually several tons ) and practically stress free driving.