...component video can pass 1080i though, and HDTV is all 1080i or less AFAIK. I would say you can live with that - considering you already bought the thing. You may be missing out on some lossless sound for hi-def movies (sometimes - not all high-def movies even have anything better than regular old Dolby Digital) as far as sound is concerned.
Lots of us have older receivers with no HDMI. I just run good old-fashioned digital optical and coaxial cables for DTS and Dolby Digital surround, and since I have the player that does it, I run 5.1 analog and let my BD player decode the lossless sound (for the discs that even have lossless sound), though I am not sure I could tell the difference in a blind test.
For video I have a separate $30 Monoprice HDMI switch that works just fine to get the 1080p signal to my display. That solution is fine IMO, and since you already bought the thing it would certainly be one way you could go.