The same signal will be displayed on both the LCD and the projector.
I can either run the component video cable directly to the 4x2 switch and bypass the receiver, or I can run the component video cables to the receiver, and then the output component of the receiver would run into the 4x2 switch (only taking up a single input on it) and it would be shown on both displays.
I guess what I'm asking is if it would be bad to have this extra "stop", if I would lose much video quality because the video would run from Voom->Receiver->Switch->Projector/LCD instead of Voom->Switch->Projector/LCD. The advantage is one less component I have to be able to control (since the switch would always be on the same input), and I get the OSD (on screen diagnostics) of the receiver since I would be using the receiver's video output (Denon AVR-3805S).