No — but what if he was? McLaren answers that question in their new Tooned cartoon.
It's not like Hunt's life needed more excitement (watch Rush and you'll see what I mean), but this alternate history is pretty great. And there is actually some precedent for a prominent athlete being a spy. I mean, just look at Moe Berg.
(Hat tip to 2bwise!)
Was James Hunt A Secret Agent For The British Government?