It depends. The factory HU in these cars more than likely doesn't contain an amplifier therefore it uses the separate one under the seat as part of the stereo system. If the one you have is a HU from another Toyota, it probably has an amplifier built into it already unless it was part of a premium sound system that had a separate amplifier. Running both of these amplifiers together is not very ideal. But either way, even if the HU you have doesn't have an amp in it already, the factory amplifier in the Supra is probably the reason you're hearing the noise. Even a few cheap aftermarket amplifiers still produce "engine noise" through the speakers. But like John said, power filters can eliminate or at least lessen this.
I was running a decent grade Alpine radio in mine but was still using the factory amplifier. I too, had the whining noise. I plan on swapping to an even better Alpine HU, bypassing the factory amplifier, and using a JL Audio 6 Channel amplifier to power the rest of the system. That should sound pretty good and cause no noise.
