That is an awesome idea, you could also use those clear plastic containers from lunch meat (Glad-Hillshire Farms) if you wanted, then they would be see through and you could easily find what you wanted!
I never thought about cutting my scraps into 2" squares, I have lots of projects that I have scraps just thrown into a bin, that is a great idea and then could easily be made into a scrappy quilt when you have enough scraps!