It certainly is possible, and with computers these days probably not unrealistic, but the source engine is really good at optimization. Basically I would have to turn off all network optimization to make split screen work properly, which would increase lag for everyone.
Portal 2 does something like splitscreen - although im not quite sure how the guys at Valve did it. (you bring up your partner's view by keeping the tab key pressed)
Either a video stream (which i doubt since it's looking too good) or rendering a second player locally based on some information transmitted via the netcode. The picture shown is small but one could scale it - maybe they developed some viable idea that'd work also for 4 players.
Example:
Frankly, I have no idea if there's some information on this out there, but just
maybe it's worth looking into it.