Nope. Once the HDMI box says "Hey I can handle it!", then it goes to put it out over the component outputs, it downsamples it to 480 to do so. This is a requirement of the HDCP specification.
Technically, there is no reason why you cannot deliver up to 1080i over a component connection. It just is being disallowed via HDCP.
By the way, you bought a TV set which is "HD Ready". I believe that "HD Ready" simply means you have to add an HD tuner to receive HD broadcasts. If the set does not have an HDMI or DVI port, it cannot meet HDCP requirements, which means it cannot display HD content at resolutions higher than 480p from a DVD player, for example.