I'm afraid I don't have a concrete answer for you, but I can tell you a few things.
- USB 2.0 spec was ratified in 2000. Adoption was pretty solid by '03, '04.
- Flash memory and the usb controllers on flash drives vary in quality greatly
- Poor quality/Cheap flash drives can offer terrible performance
- You're not really gonna know for sure until you actually try another drive
I'm pretty sure you'll see at least some improvement with a new drive, mostly because usb 1.0 is incredibly slow, and a usb 1.0 flash drive probably has some pretty old and crappy flash memory in it. I'd almost go as far as saying that even if the car isn't 2.0 (my guess is that it is), a modern 2.0 flash drive will have much better flash and will probably perform better than what you have even in a 1.0 slot.
My suggestion is to just borrow a friends thumb drive, that should at least give you a good indication.