There is no official rules on what cars are allowed in the show area.
Basically I look at it like this. If I show up with whatever I happen to be driving that morning and decide to park it in the show area. Do I feel ok with myself if a one of the kind Ferrari, Bizarinni or whatever gets turned away because I parked a fairly pedestrian car in the show area.
There is a spectator parking area which you will find very nice and expensive cars which their owners don’t believe to be show area worthy (AMGs, M’s, Turbo this super that) and every other sedan and sportscar. In my own very very very humble opinion your friend’s Vette should probably be parked in the spectators area and you have a couple more months where the 370Z Roadster is still novel enough to park in the show area if you want but that is my jaded view.
In the end it is up to you. cheers!