Think it's fine to put down FRA in the entries, although I don't think the FRA are affiliated for the roads, so thats about as legal as me putting Pony down on road races. Nobody seems to object though.
You can be a Pony with out the vest, or indeed make your own. Helps for recognition of fellow nags in races, and "membership" is otherwise what you make of it; nothing or an awful lot. The vest helps as a conversation piece, normally along the lines of "what the f__s that". God knows what they make of Fleeter's little pink number