As the title says.
Also, what level of programming would be required?
I have never coded anything for Blender, but the answer is Yes, if you are an expert programmer in C++ and Python you could turn blender into a web browser. My question is why would you want to do that? What are you trying to accomplish?
I think the idea would be if Blender could navigate online file repositories, Blendswap for instance, (append–>>Blendswap) then Blender can navigate blendswaps repository, or adding sounds from freesound or soundcloud, etc