Yes, as long as your kernel is new enough to support Docker (and that of 14.04 is) then your Docker container will run on it, no matter what the base image is.

Yes, as long as your kernel is new enough to support Docker (and that of 14.04 is) then your Docker container will run on it, no matter what the base image is. This is thanks to Linux' relentless binary API backwards compatibility. The only thing your container interacts with is the kernel, and the API of the kernel never changes, so it'll run on any Linux operating system that's new enough to run Docker at all (and is 64-bit).