Sorry you are incorrect. As AV_Mike said, the voltage at the amp output will be full range but not the current. Consider this, if you have the amp turned on but the speaker wires disconnected at the speaker terminals so the impedance seen by the amp is infinite and you would agree that current will be zero meaning there will be no signal flow in the wires right? Similarly, the high impedance imposed by the high pass filter of the tweeter/crossover will limit the lower frequency signals so the amp is unable to send a full range signal. Remember current flows need a complete path, i.e. 2 wires, the amp just cannot send a low frequency signal to the speaker terminal with no return path. So if it gets blocked due to the high impedance of that particular frequency, there will no flow, period. Of course in reality filters are not brick walls so they don't block 100% of any unwanted signal.
I understand this concept is not always easy to understand unless one has a solid background in electrical circuit theories but it is a fact. Don't believe me, but ask someone you know who teaches circuit theory or EE friends who know circuit theory well.
I am saying that a full range signal is sent from the AVR, which it is. What happens downstream isn't relevant to this discussion, although clearly you are right that if the speakers are disconnected zero signal will flow. The point is, which you seem to be missing, that the passive biamping of the speakers serves no purpose because proper biamping requires an active crossover between the pre and power amps, which is not the case in the situation under discussion. Similarly, removal of the speaker jumper straps will not somehow bring about biamping and will not cause the signal from the AVR to be split in frequencies in any way at all - hence the assertion that a full range signal is being sent. The technical considerations you mention are interesting but not relevant to the matter at hand.