That's what I'm doing, tho truth be told, I won't know if it's a novelette, novella, or novel until I'm done, and as for "great"...well, that's not my call to make. I got a smartphone, a Motorola/Android, because I hate down time.
For me, down town consists of all those times I'm away from a keyboard & can't easily write notes (sure, I can & have used pen & paper but then it has to be re-typed into my computer & it's the rare occasion when there's only notes to one topic on one piece of paper -- or for that matter, the paper is of the same size).
My first use of the smartphone was to forward online articles to myself so I could read 'em while waiting to pick up Soon-ok after work or when on the recumbent bike in the gym. I also looked at old TV shows or cartoons when I went to bed.
But recently I've started working on a new story on the smartphone. It progresses in bits and pieces -- 30 minutes on the bike, 5 minutes while waiting for Soon-ok, 10-15 minutes before dropping off to sleep.
But it's getting done. The story is briskly moving forward and while entering text via tiny smarthphone keyboard isn't as fast or as easy as my desktop's, it doesn't prove to be an insurmountable hurdle.
So from time to time I'll post updates on my progress, letting you know where I'm at & how the experience differs from regular writing.
(It's not like this hasn't been done before...)