Can you put a ATi Radeon X800 Platinum XT into a Alienware 51-m laptop?

No.

It's too large, far too hot and would drain the battery very quickly.
This means you're forced to use a slow yet expensive laptop card. A
Radeon Mobility 9800 is likely to be the best you'll get, with full
DX9 support and 128mb VRAM but it won't match one of the new next-gen
cards.

If your laptop is quite new it should support Alienware's new
replacement system which lets you send for a screw-in module
containing a better graphics card.

thank you that helps a lot

if you do have the user-upgradable graphics, does it make it possible
to use the X800 then, or will it just not ever work with a laptop?

One day there will be a mobile version of X800 but it won't be as fast
as the desktop version, due to the reduced power supply and heat
tolerance and of course the small size.

If you plan to upgrade you should wait to either it or the 6800 gets a
mobile version.