I have a Supertooth II that I'm using with my 8300. The manual doesn't specifically mention that it supports the Curve, but lists other Blackberrys. It does state that it requires a manual connection:
After turning the Supertooth off, or going out of range, to reconnect just press the Pick-Up/Hang-Up button on the Supertooth once.
Problem is, that also activates the voice dialing and you have to cancel out of that. It is somewhat cumbersome and not as you would expect the pairing to work.