yes the apps you purchased will run on the xoom, however depending on how the dev coded it, it could look a little wierd. for example if they used vector graphics (most games do) then it will look fine (just really big). however if the app uses static pictures (alot of live wallpapers do) then they will look very pixelated. what the xoom will do is simply scale up the image. the best way to describe this would be to take a picture that is 800x480 (standard android 2.1 and 2.2 high resolution) and then go to MS paint or a picture program and change the image size to 1280x800, that is basically what will happen.
with apps though if they are using menus and bars instead of pictures for the UI it wil scale up just fine because those menu bars and buttons are created by the app calling the android OS to create a bar, the honeycomb OS knows your xoom screen is 1280x800 and will draw it correctly. however one thing you will notice is that some will look funny because of the design. for example if you take the "movies" app, looks great on a phone having those divider lines and bars between the showtimes and reviews, imagine that bar running from one edge of the xoom to the other. it will render fine (no pixelation) but it will just look kinda odd since a line running across a phone looks great, across a 10" tablet looks odd.
when you hear them talk about apps for tablets, they are not saying only these new apps will work the old ones will work just fine. the new apps though are designed for a larger screen, so in our example "movies" comes out with a tablet app and those bars and lines don't run across the screen in that app they stop half way and maybe have some more info on the screen etc... if you have seen the video of gmail running on the xoom, that is an example of an app made for a tablet because it uses "fragments"(<-googles word not mine, web developers simply call these "frames") of the large screen for different sections of information. if you see that video and then look at gmail on your phone you will see what i am talking about. now the version of gmail on your phone would work on the xoom but imagine how funny that would look stretched across the xoom and you see why they wrote a tablet version of gmail, not so that it works so that it looks better and takes advantage of the large screen.
woo that was long winded, hope that helps