I have a similar BT module. Mine is a JY-MCU. The short answer to your question is yes, but it would be tough.
If you connected it directly to the rx/tx (pins 1 and 2) of the arduino you could theoretically upload code. However, in order to do that you would need be able to reset the arduino. You can try it out by just pressing reset right before you press upload. Or you could build a circuit to reset the board for you, perhaps you could do this more easily with 2 Arduinos.
Many people before you have tried it, see this forum post and 9Vortex's trials: http://arduino.cc/forum/index.php?topic=111478.0