2011 Mazda 3 - will I have any problems installing both a hitch receiver and a Corksport rear sway bar at the same time?

What it says in the title. I'm wanting to install both a hitch receiver (for a bike rack) and a Corksport rear sway bar. Has anyone else done this? Am I likely to run into problems mounting both at the same time? I don't really know mechanical stuff. I just want to make sure everything will work out before I order the parts and take them to the garage for installation.

The vehicle is a 2011 Mazda 3 S Grand Touring hatchback (2.5L 6MT).