Yes but not like that. I have 2 belt-drive bikes with internal hub gears. For a utilitarian city bike, I think there's nothing better and they will be much more common as more people try them.

List of benefits:

• Basically no maintenance required. You might need a yearly oil change.
• You can change gears while stopped
• Nothing oily to get your pants dirty
• Virtually silent. The ones I have don't even click while free-wheeling.

Downsides:

• Most internal hub or gearbox transmissions don't like changing gears under load
• They're heavier than a chain and derailer setup
• They're generally more expensive
• They require a frame that can split somewhere in the right side chain or seat stay. This isn't a problem if you get a bike with a belt but it makes it pretty much impossible to convert an existing bike
• To change your transmission, you need a whole new wheel (or de-lace, and re-lace your existing wheel).
• There are fewer options.
• Generally, you have fewer gears