You're right, the picture from the native 640x320 projector probably won't look HD.
Whenever a signal's resolution doesn't match a projector's native resolution, the signal must be scaled up or down to match the projector's native resolution before it can be projected. So, the 640x320 native resolution projector would need to scale the 1080p HD signal down to 640x320 before it could project it, and during that scaling process some sharpness would be lost. I'm guessing the comparative difference in quality would be pretty noticeable at a large size like 60".
Here are a couple sources for some of the above:
On a side note, the fact that the native 640x320 projector can still play a scaled-down 1080p signal is probably what entitles the projector manufacturer to say that the projector "supports" 1080p, even if the picture isn't as good as on a native 1080p projector. No doubt this is a source of confusion for projector shoppers everywhere...