When using an Integrated Amp with HT Bypass for 2 Channel - The AV amp is side-lined and thus plays no part, as the 2 Channel source is plugged directly into the Stereo Amp (which is connected to the the FR and FL speakers).Coming to the issue of adding a 2 channel integrated amp with HT bypass. Ive tried that too. But unless your speakers are very inefficent it is pointless doing so in my humble books. The clarity and detail retreival are done at the dac and premap stage both of which are built into the AVR. So adding an external poweramp doesnt change anything. My system was a Marantz SR 6011 feeding a parasound halo integrated + Qacoustics concept 40 HT system.
When playing Multi-channel, the Pre of the Integrated amp is bypassed, so the Power Amp section (which is now replacing 2 Power amps in the AV Amp) drives the FR and FL channels using the AV amp as a Pre.
The result: You are using the Integrated Amp for Stereo as normal and the AV Amp for multi-channel (though the FR and FL channels are routed through the Stereo Power amp section).