Some places can handle a large group (that is, folks arriving and eating at the same time) on separate checks; others can't. They run cards more than once, mix up charges and orders, can't deliver food except one order at a time, etc.
I suggest that whoever plants the flag for a gathering pick a place that's done well in the past, or call them, explain the EXACT situation and ask if everyone can get served more or less simultaneously and if separate checks will cause them any problems. I'd emphasize the business and the minor draw of having all these cool cars in their lot...