Yes, it's possible... No, it wouldn't work well at all.
First look at memory usage. The N64 has a unified memory model, which means that it's shared by everything. So say you start with the standard-issue 4megabytes of RDRAM.
First you'll need a framebuffer. And you'll need two for double-buffering. So, two lo-res 320x240 16bit CFBs will consume 0.3MB. And since you'll never be able to fit anything meaningful in that screen size, let's look at 640x480, which will take up 1.2mb.
Down to 2.8MB for everything else - overhead including buffers, fifos and displaylists will probably take up another 0.5MB.
So you have 2.3MB with which you need to render a website.
And then you'd need to find some way to get the data into the console. Would probably work best to buffer network data and have it fetched over the cart PI interface.
A royal pain.
Seriously though, I've thought about doing some sort of system link between two consoles. They would communicate over a controller port on each, and a MCU between the two. Would only work for my own games, of course.