Genk is a great track, you should definitely see it if you can. According to the calendar on their web site (www.kartinggenk.be -- only in Dutch and French), the track is closed to the public the entire week of August 29 - Sept 4 for the World Championships. They do state that the restaurant and rental karts are available, so you will have access. I can't be sure if the teams will be running on Monday but would guess they will. (The restaurant is pretty fine too -- it's gourmet by kart track restaurant standards! -- and has a huge terrace from which you can see about 95% of the track.)
Are you all set for Spa? I've never been there for the F1 race, but another American is a regular and knows a budget priced B&B in a good location.
If you have time, you should also check out Kerpen, the track that Schumacher grew up racing at (and still does) -- www.kart-club-kerpen.de. And then of course Kerpen is only about an hour from the Nuerburgring . . . (Just don't try taking your rental car around the ring - the agencies use the GPS to track it and will ban you for life.)
My son and I may go to Spa and/or Genk, so maybe we can meet up.