Many if not most of the Sega references throughout Shenmue exist outside of the timeline of the plot. There's a Saturn... you can win games for it at one of the stores. There are capsule toys referencing games that came out years later as well. Not to mention the nonexistent Sega items, such as the Master System notepad in one of Ryo's drawers, and even mystifying items that reference Shenmue itself, like Shenhua caramels available at the store. This kind of stuff is so woven into the details of Shenmue that I don't think I'd personally classify all of these things as easter eggs, but either way... it's all there in the world.
More specific to the original topic - Genesis games in Shenmue 3. Beyond whatever licensing considerations there might be with Sega - why not? It would fit with the established "rules" of the game world. The only thing is, the Genesis library has been re-issued time and time again over the years. It would be cool to give the Master System some love, or various other Yu Suzuki arcade titles that haven't been featured in Shenmue yet.