Yes. Due to copy protection, an HDMI input source switched to a component output source will result in either a blank screen or downconversion to 480. I personally do not know of a component (i.e. a receiver) that will do HDMI->component. Usually they are component->HDMI only.
Actually, your original question is really unclear.
HDMI input -> component output is nonsensical. The output of a source goes to the input of another device, not the other way around. Exactly which equipment are you trying to connect, with exactly which jacks? Are you trying to use one of those HDMI->component converters that circumvent the HDCP (with hazy legality)?
Or are you merely asking what happens using component connections instead of HDMI connections?
There is at least one HDMI->RGBHV converter on the market that supports 1080p outputs. It's a small "dongal" sort of thing that is meant to screw onto your display's input. It was in the neighborhood of US$400, I think, and would handle the HDCP exchanges and handshakes.
I found it once before; I imagine I could find it again - particularly when I get to work again and check my e-mail archives.