Yes this IS possible using an interface very similar to HomeBrewBrowser and setting up your own server that stores the wads etc.
However everyone I know that could code something like this wont take the time to do it.
I could probably write an app that does this, but I wouldn't dare release it as the server would be pulled very quickly and my time and effort would be wasted.
If you want something like this I'm afraid you would need to code it yourself, or wait patiently until someone else releases an app.
Oh and not using the internet browser as that cant write to the SD, so you would need to write an app that goes to a site, lists contents and allows you to select a file, once selected it would need to download to SD and then unrar, not impossible, very hard though.