Are tow-hitch bike racks legal?
This will be state depended, and the law enforcement response is likely very localized (down to individual officer responses). 

Where I live (outside US) it is illegal to have the numberplate obscured. We have a choice to either temporarily relocate the plate, or we can buy a Supplementary plate. In both cases we have no obligation for number plate lighting provided the main plate is in it's correct place when that is not obscured. As far as local law enforcement - the only problem is you will get pinged rarely - usually a cop who has not got his ticket quota this month. 

Many people print there numberplate onto a piece of card and use that - whilst not legal I have not heard of anyone being ticketed for doing it, but i have heard of people being ticketed for not having anything. 

Best option is talk to a local bike shop - the one you are buying the rack from - and ask them.