Is it possible to improve by playing mostly blitz? Can you improve significantly in chess by playing mostly blitz (say, 3 0) games? Or will you eventually reach a wall where the only way to advance is by sitting down for lengthy periods analyzing board positions? 

The way I see it, blitz is good because:


Lots of in-game experience
Board vision
Quick tactics practice


What's say chessexchange?
Blitz is good for working out the kinks in an opening repertoire and reinforcing themes that you already know, but it won't help if you want to learn new tactics or ideas.

Blitz is too fast to be conducive to figuring out new plans, especially 3 0.  

There are some upsides to blitz, though.  First and foremost, blitz is fun!  If you have 20 minutes, a few blitz games are probably going to be more enjoyable than digging up an old master game and slogging through that.  If you go over blitz games afterwards, you'll definitely learn more about your openings as well.  

In terms of reinforcing themes and working on tactics, if you make an honest effort during the game to look for the best move and work out the complications (as opposed to just making speculative sacrifices), then yes, it can be useful.

So to summarize, nothing quite compares to going over games between two grandmasters, but blitz isn't terrible.  Make sure that when you do end up playing slow games you settle down and think long enough on every move.