Would connecting an amplified sound output to a line level input(aux cable) affect my car's stereo speakers negatively?
That would depend on your definition of a problem and how well your car stereo is designed to handle over-voltage signal inputs and if your speakers are rated high enough to handle the sustained MAX power the amplifier can put out.

Chances are one of those is not, so yes you could easily blow the amp or tear a speaker.

Even if everything can handle it, it is still not a good idea. 

The aux input is expecting millivolt signals, not volts. The amplifier with quickly rail-out, and all you are going to hear is a LOUD noise.

You COULD use a resistor divider to "de-amplify" the blue-tooth output before you feed it in, but you will get a loss of quality along the way.