Unlikely.
Most generic bluetooth dongles require drivers to work on different systems. A windows computer, for example, would have drivers to work with this type of software. Often they're provided on a disc with the hardware. A car stereo, however, doesn't not usually support software installation.
The best option would be a dongle like the image below. The most simple setup would be to plug it into a 3.5mm AUX jack on the front of the stereo (assuming you have one) and also into the USB port. The USB port would only provide power, and the 3.5 TRS would carry the audio signal. You could still use a wireless connection between your phone and stereo this way.
Additionally, if you want something that looks a little more elegant, most head units provide ports on the back of the device where you can input a signal. You might need a 3.5mm -> RCA adapter depending on what sort of plugs your head unit has. Then, you could attach a 12v -> 5v step down to the bluetooth unit for power, and hide everything away behind the dash. You might want to have the dongle somewhere that's occasionally accessible like inside the glovebox, for pairing.
I have a similar setup in my car and it works really well. You should be able to pickup both items for about $20 or less.

