This is exactly the model that my team uses. We have ~40 folks on-site in SF, and about a half-dozen who work remotely. We got a Double a few weeks back, and after a slow start it's now in use most of the time.
The OP is not wrong about the qualitative difference between a 'bot and a normal video-conference setup. Things like this may seem minor (or even silly), but they go a long way to make it feel like our remote colleagues are actually present and part of the team:
https://twitter.com/thedeepg/status/337352680840257536 https://twitter.com/rcoder/status/336584756147916800