Any HD screen will take an HD signal, but not necessarily 1080p. If your screen hasn't got 1080p resolution, you can send HD as 720p/1080i. For the record, the arguments over the difference between 1080p and 1080i continue to rage, so it's certainly not accepted that 1080p is better. Also, a surprising number of screens that don't have Full HD resolution can still accept 1080p signals, downscaling the content itself.
As is pointed out above, we're yet to see a 32in 1080p TV, and when we will or more pertinently whether it will be worthwhile, is certainly debatable. Regardless, from the screens we've seen, it's clear that resolution is not the be all and end all. Nearly all our class-leading screens recently have been lower resolutions than others in the test, so it certainly seems that Full HD is far from a necessity at the moment.
In answer to your question, the Samsung can't display true 1080p pictures. But your HD DVD player will be able to send out a 720p/1080i signal that your screen can deal with and may well be every bit as good.