To echo the other responses here, you sure can!

I did essentially the same thing. I started with some Crank Bros Egg Beaters on my mountain bike. Switched them to the road bike when I bought it, and used some platforms on the mountain bike for a while. Got fed up with them, so have just bought a set of Candy SLs for the mountain bike. Egg Beaters have been great on the road bike - I have the stainless steel versions which are reasonably light weight. A friend of mine has used Shimano M515s on his road bike for the last year or so, and is very satisfied with them.

If you get some stiff sole mountain bike shoes, you can use the standard egg beater cleats and have arguably as good a setup as with a true road shoe. Or buy a road shoe, and spend another $20-25 on the EB road cleats. They are much easier to walk in than most road cleats, and the release on mountain pedals is usually much easier than road pedals (good for riding around town when you need to click out frequently).

You can pick up Egg Beater S pedals off ebay at the moment for around $65-80 (retail $140).