Nope. When you get gold, you get the money payout for the gold time, the silver time, and the bronze time. When you get bronze, you just get the bronze payout. When you get silver, you get the silver and bronze payout. If you do them consecutively, bronze, then silver, then gold, you get the same amount of money because you're only still getting the payout for each one.
Also, *MOST* time trial events online DO NOT award you a prize car. At least they generally didn't in GT5. I believe the only ones in GT6 to do so have been the Hudson event and the M4 event. Might be forgetting one or two, though...
In GT5, the events you could do over and over for the payouts were the seasonal race events, not the drift or time trial events; those were one-shot deals with payouts for bronze, silver, and gold times only once each.