They only use that petty stuff as an excuse to check you out if your otherwise suspicious, fitting a description, or fitting a general profile (AKA "profileing", dirty old car in a rich neigborhood, or black guy in a rich neigborhood, etc. it happens daily)
the bike it's self will cause no problems, I have driven some 30,000 plus miles through a dozen states and 3 canadian provinces/territories with rear mounted bikes. the rack I use is a trunk rack for older cars that actually have trunks so it doesn't block too much.