Like A1GP which didn't last long...not sure how this would last all that long
Well this isn't a spec series that's going up against Formula 1 during their off season, this is a one off event involving a huge array of different manufacturers that only show up for one event. Admittedly easier to put together.
Since we're speculating, here's my list of what cars and teams each country would run, some of the larger countries will get two teams and cars representing them (I will include speculated cars like the Cadillac and Porsche 991/911 GT3-R):
United States - Viper GT3-R/Riley Tech, Cadillac ATS-V.R/Pratt & Miller
OR Ferrari 458 GT3
-Audi R8 LMS ultra/DragonSpeed Racing
OR McLaren 650S GT3
-Audi R8 LMS ultra/United Autosports
Canada - Viper GT3-R/Riley Tech
United Kingdom - Bentley Continental/M-Sport Bentley, Aston Martin Vantage V12 GT3/Aston Martin Racing
Germany - Mercedes SLS AMG GT3/HTP Motorsport, Porsche 911 GT3-R/Wochenspiegel Manthey
Scotland (?) - BMW Z4 GT3/Ecurie Ecosse
Belgium - Audi R8 LMS Ultra/Belgian Audi Club WRT, BMW Z4 GT3/Marc VDS
Netherlands - Callaway-Chevrolet Corvette C7/V8 Racing
Denmark - Aston Martin Vantage V12 GT3/Aston Martin Racing
Austria - Lamborghini Huracan GT3/Grasser Racing
Switzerland - Lamborghini Huracan GT3/Blancpain Racing, Maserati GranTurismo GT3/Team Swiss
OR Emil Frey Jaguar GT3/Emil Frey Racing
Brazil - BMW Z4 GT3/BMW Sports Team Brazil
Russia - Audi R8 LMS ultra/G-Drive Racing, Ferrari 458 GT3/SMP Racing Russian Bears
Spain - Porsche 911 GT3-R/Drivex School, Nissan GT-R NISMO GT3/Team RJN
Italy - Ferrari 458 GT3/AF Corse, BMW Z4 GT3/ROAL Motorsports
France - McLaren 650S GT3/ART Grand Prix, BMW Z4 GT3/TDS Racing
Australia - Mercedes SLS AMG GT3/Erebus Motorsport, Lamborghini Huracan GT3/Lago Racing
New Zealand - McLaren 650S GT3/Von Ryan Racing
Hong Kong - Aston Martin Vantage V12 GT3/Craft-Bamboo AMR
Japan - Nissan GT-R NISMO GT3/B-MAX Racing Team, Lexus RC-F GT3/------
This is obviously a pretty rough guess. I'm not sure how crazy they would allow foreign teams to represent other countries (ex: Riley Tech running a Canadian Viper or AMR running a Danish Vantage?) I think if they didn't it would limit the field too greatly, though.
These are most of the cars and teams that I've noticed have strong links to their countries and drivers they use tend to be from that country. In the case of the US, obviously Riley Tech and Pratt & Miller would be the shoe-in teams to represent the US... but would they be likely to travel abroad? DragonSpeed, albeit a smaller team, has had eyes on heading to Europe and so could represent the US, and United Autosports is based in the UK and is a pretty well established GT3 team. So there are questions there.