I don't know much on the subject, but I did just get to see what is claimed to be a Mk II GT40 Road Car yesterday, one of ~30 made. I assumed this (or something similar) is what the car in GT2 was based on.
That's a Mk I despite what the top of the sign says, the Mk II was the Shelby-developed 7-litre car. A lot of them certainly were road-registered, but the 30 cars figure just refers to cars that were fitted with any of the more road-friendly upgrades like carpets or stylish wire wheels. Quite a few of those 30 were still raced anyway, and some of the race cars without those options were never raced and only used as impractical road cars.
What muddies the waters in GT2 is that the car depicted has some road-biased elements like the lower-powered engine and wire wheels, but then it also has some race upgrades like extra vents from the John Wyer racecars, and is very deliberately set up as a race car with pre-purchased tyres, slicks by default, no upgrades, and no RM. The description claims it's sourced from 'the last' GT40 built, but anything meeting that description was generally a race car. Personally, I think the car it looks to be most inspired by is P/1069, a famous press car with the wire wheels, but that has also been raced before being restored back to the press car look fairly recently.
The GT40s in general seem to be have been pretty confused during GT2's development, with the John Wyer car being listed as a Mk III for a while before PD realised it's just a modified Mk I. I suspect at some point they also thought of it as the race version of the 'road' GT40 hence the deleted RM, but by release they'd figured out that the plainer car is a 1966-ish car and the Gulf one is a 1968-1969 car.
Ultimately, to overrule how Polyphony set it up and say that they're wrong about it being a race car needs some pretty solid evidence, and I'm not sure if we really have that. I think it's pretty likely that PD planned to set it up as a road car initially, which would explain the wire wheels, unfinished RM and the Rome Historic oversight where it's the only car with racing tyres, but it was very deliberately changed to a race car before release (although they missed the R prefix in the replay name). It'll probably stay a race car for now, as I think it'd be a bit silly to say 'yes, this is a standard road car' when it comes on slicks. However, I'm debating whether to give it road-compound tyres at some point to fix the Rome oversight and make it drive more like a 60s car on the default tyres, but that might end up being a change only for the Complete version as it's not necessarily just a bugfix.