I understand the caution and it's a nice, respectable thing. I also think it's important not to make other people feel bad. If I was concerned about it, I'd treat the 27'' machine as something everyone can enjoy.
When it comes time to put the books away for a bit, you and your machine will deliver the best, funny youtube clips. For the whole room.
Or if theres a bit more time, and everyone's studies are done, and its after normal study time you can throw in a quick movie that everyone will enjoy right there on the spot.
Instead of your study mates thinking it's just your over-the-top computer, make it as something that is there for everyone and they'll see it as the go-to point when someone or everyone really needs to something clearly, or just wants to relax. Because its more useful and would bring some extra fun to the room this could actually help create a good perception.
Hey, great point!