They won't update, some of them won't launch, they may not put their support files in the right place and basically it's a really dumb thing to do*, so don't do it. Use aliases if you like.
*Five reasons why putting anything on the desktop (other than temporarily) is dumb:
1. It looks unprofessional. Sooner or later you are going to need or want to show off your screen in public. Don't look like a five-year-old who can't clean his room.
2. It hides your beautiful wallpaper/desktop picture. Why on earth would you want to do that?
3. It breeds sloppiness. One file leads to more files, before long you have tons of files on there, can't find anything and have to use workarounds to get anything done.
4. It slows the machine down. Large quantities of files on the desktop will actually consume processor resources, since the desktop (unlike the rest of the computer) is updated constantly.
5. Too easy to accidentally throw something away. If you throw away an alias by accident, who cares? But if you throw away the original app and don't notice till you've emptied the trash, that can cause major havoc -- since it will always happen at the worst possible time.
There's nothing wrong with using aliases on the desktop if you want, or the dock, or temporarily putting a downloaded or dragged file on the desktop for immediate use. But for the reasons I've mentioned and many others, UNIX (the foundation of OS X) does impose a LITTLE BIT of structure on us in order to run more efficiently. Respect the structure and keep your desktop clean.