Technically you could totally do that, it's already a feature in the game (one of the hot-keys on the F3 screen) to not pause while out of focus. But I agree, kinda silly ^_^The only way for that to work is to keep the game running in the background, which sounds like a terrible idea for multiple reasons.
On a side note that's related but not related. You could create a "Macro" robot
Hold a recording device, and perform a series of actions (movement, left clicks and right clicks - nothing too complicated) Then use the programming table to program the recording into the robot.
Once activated the robot will go from it's dock, to the starting point of the macro, carry it out, then return to the dock.
With some simple redstone/pulser/gate commands you could automate a process that normally requires more interaction than redstone can accomplish!