How do you define "juice"?- Volts? Amps? Amp-hours?
For a start, you Uno needs either 5V at the USB input, or 7+ at the barrel or Vin, so you're already going to have to regulate your 6V down to 5 or up to 7.... Although I'm assuming the Uno needs to be powered from those batteries?, or will it remain hooked up to the PC on the USB?
Then that motor shield uses a 298, which eats volts.... from memory, and you will need to check the data sheet, it drops a minimum of 2V up to 3 or so depending on current, so you need to put at least 2 more volts in than your motors need... you didn't say what they are: if they're toy types at say 3V then you could be ok.
And the servo will need 6V.
You'll need to do some sums as to what current you need for all of these things.....