Trunk bike carrier

I have a new 16' Bambi Sport with a Husky Centerline WD and Sway control setup pulled by a 2015 Toyota Highlander XLE. As you know, the Bambi Sport has no back number, so putting a bike rack on the back is not an option. However, I was wondering if using a trunk type bike rack (Yakima KingJoe Pro) on the back of the Highlander while pulling the airstream will cause problems. I am thinking specifically of issues with turning, limiting the turning radius, especially when backing up.