No ... is the short answer. The longer answer is Yes, IF it is a dual format disc.
Some HD DVD's come with both the "Standard DVD" and "HD DVD" versions on a single disc. Meaning that the disc can be used in both players. But Standard DVD players cannot play HD DVD content.
BTW, this "Dual Format" ability is one of the distinct advantages to the HD DVD format that Blu-ray has yet to conquer. Due to the way in which the discs are constructed (i.e. the way the sandwich is made), HD DVD's lend themselves MUCH better to containing both formats.
I hope that didn't confuse.
- Shane