Is it possible to capture a 433MHz RF signal using the PC bluetooth?
No.

One reason is getting the whip antenna for the bluetooth to accept such a "low frequency" signal requires hardware modification and re-tuning of the reception circuitry, since BT is 2.4GHz.

Another reason, even if you'd get the chip to accept the lower centre band frequency is that the encoding scheme and signalling bands on both protocols are vastly different, so it would make no sense at all to the chip that is hard-wired for BT.