Too much upconversion?

I now see DVD players, A/V receivers and HDTVs that will upsample a 480i input to 720p output. If they were all used together would the final video signal be compromised by "over-processing"? Can you bypass the upsampling and just let one component do the conversion?
No. because once upsampled to 720p the next device will simply pass it through without upsampling any further.
Unless your display doesn't do 720p natively. Ideally, you want to your video to be deinterlaced and scaled only one time each. If your native display is not 720p, it would be best to have a processor scale it from 480i or 480p to the native display rate. Going to 720p and then to the native rate of your display may or may not be an improvement over running 480i/p into your display depending on how the quality of the display's scaler is.