This brings up a second question, will WSI allow you to choose your own vendor? Like Allisonhouse.com for example ? Although you probably won't get the RPM model?
No you can't use any data not provided by WSI (with a few minor exceptions)
Essentially WSI sends out special data feeds of model data and current conditions. Those special grids are sent to the Core and then sent to the MAX system.
Also live sweeping radar is not included unless you buy MAX Storm. I'm sure that is another expensive package and monthly fee. The base MAX system does have a radar mosaic like you see on TWC but its pretty poor quality when you are really zoomed in.
These systems are intended mostly for tv stations which is why they can charge such a high rate. Larger TV corporations sometimes negotiate rates for data and systems so its a bit cheaper.
I use MAX everyday at work and it really is an amazing system. It's super powerful and very flexible. The only software that came close to it was WeatherCentral... which of course was bought by WSI and being phased out as they integrate Weather Central features into MAX.