The short answer is yes it would work, but is not the most practical. It would be better with a plugged in USB hub into the back of the chromebit, but still not ideal. Chomebit is designed for Bluetooth connected keyboard and mouse.
It's been a while since I used my Pi. But I do remember having to jump through a couple of hoops with Logitech's Unifying software but I did finally get it to work with some scripting I found online. I would assume this combo would also need the same help.