I don't remember what it was called, but during a training meeting at my old job, we played a game where one person wrote a sentence on a piece of paper, then handed it to another person who proceeded to draw a picture of what that person described. The person who drew then gave the paper to the next person, who could only look at the picture and write what they thought it was, then handed it to the next person who could only see what the person before had written and draw a picture of it, and so on and so forth. It was basically a mix of telephone and pictionary.
Anyway, I think Draw Something could easily offer this as a variation of the core game, just by having more than two players, keeping things hidden from certain players at certain times, and adding an option to simply input text, so that no one has to read chicken scratch.
Maybe they have and I just don't know, but I thought the game was fun.
Just a random thought before I write another blog.
if i could make all the games I come up with I would be one busy dude. busy, but happy. 
There are free app developers, I believe, and I know for sure there are free programs teaching how to make apps, so if your ideas would suit that format, I'd say go for it.
ah, I've messed around with Unity and RPGmaker among others, and it's really fun but more work than I have time for as I have other projects. I'm going to get back into it though, it's very entertaining.
There is a mini-game in Game & Wariio called Sketch, and there's an online version called Miiverse Sketch that's kind of like what you're describing.
Yeah, I kinda figured someone had done this already, but I wish I knew where to find a version I could play.
Sounds like something that could've worked on THQ's UTab drawing device that came out a couple of years ago. To bad the device tanked and the company folded =(
I remember reading a Cracked article about that thing being one of the pitfalls that led to their demise. Hadn't heard of it otherwise. And that's why advertising exists.