A cheap sound card can affect the sound, as it picks up other frequencies caused by the CPU/hard drive,etc.
Its why I always opt for a proper PCI one that has shielding, etc.
If you are porting USB to your car stereo though, its digital, so no, you won't affect the sound with a cheaper one AT ALL.
Its sending 0's, and 1's, to the stereo and nothing more. Nothing can be lost or changed.
Only if it is corrupted data will you get issues, which may be an issue for a really cheap one, but not any more I wouldn't think.
The sound then goes to the DAC of the car stereo which then changes the sound from digital to an analog form for output to the car speakers, which then passes to the interal AMP which amps the low signal to a higher one for transmitting. THIS, is where the sound can change, if the DAC isn't very good, and the amp of course also makes a difference, as the amp itself can change the actual sound.
If you are serious about car audio, its actually best to buy an external amp to give your speakers the best output (at least if they are aftermarket ones)