Will I overtrain my legs by running on the days prior to and after my leg training day?
Depends. If you run a marathon, then yes. If you run a mile or two, then no. If you are not eating much, then yes. If you’re carbed to the gills, then likely no. How much do you plan to run? Can’t answer the question without that information, diet information and training history information (i.e., have you run before?, any problems?, what do you do on leg day?)
Sprinting? Yes. Jogging for short to moderate distances. Probably not.
Running/jogging was my 1st love since 1982, in summer of 1999 I added wts. On leg day, I habitually did not run until after the trashing of my legs (20 mins. or so) Short durations (bout 1/2 hr. for me) seems o.k. Just don’t do 10 miles the day after–not safe. Almost wobbled into a forklift at work.