iPhone 2g screen replacement question

I've done my research and I know that iphone 2g LCD screen, digitizer, and glass are all "fused" together so you have to replace everything if something with the screen breaks. I've seen on eBay that you can buy an LCD screen for 2g and you can also buy a digitizer with glass screen. Buying these elements separately and putting them together is cheaper than buying a complete LCD, digitizer, and glass screen unit. So, I would take my old iphone screen completely out, and put in a new LCD and separate digitizer/glass unit to make a complete screen. My question is, has anyone done it this way? Does it work?