Eventually. Although I did have a Genesis growing up, it always played second fiddle to my SNES, so back in the day, I only had about 30 games for it in total. Even now in my adulthood, fate still conspires against me with none of the local used game stores near me selling ANYTHING sega, with the reasoning "Sega games don't sell".
My only source for sega games are conventions I attend and ebay. As a result, I don't know the library nearly as much as I do other systems. I can talk about obscure gems like Zero Wing, Alisia Dragoon or the brilliance of the Micky Mouse platformer, but you guys deserve someone who can tell you about games you DON'T know, and as of right now, that's not me for Megadrive.
After the GB list is finished up, I can do GameBoy Advance, SNES, Xbox (1) and perhaps a few others. The next list will most likely be for GBA, as that's most logical.