Video analog to digital upconversion delay or lag

Many budget (sub $500) receivers now do analog to digital conversion/upscaling to HDMI. Does this process introduce a delay in the video? I am concerned that if I connect my Xbox 360 to a Yamaha RX-V665 or Onkyo TX-SR607 with component video cables and allow it to upscale/convert to HDMI (to minimize cables ran to tv or projector) that my reaction times will be exaggerated because the video is delayed by the conversion process. How much delay--if any--is introduced? Thanks,

I had forgotten about the fact that my tv or projector would no longer have to do the conversion... The delay may not be any more than it is now, depending on how intense the processes are comparatively; like if the tv or projector doesn't do any sort of "upconversion" while doing the analog-to-digital, it may be a few milliseconds faster than the receiver. Would I notice that? Most likely not, unless it is a very technical fighting game (which I don't play much). I wish figures like this were published, but perhaps they are so small, it doesn't make much difference. Thanks for the insight,