Not really. I assume the 7.4V batteries are NIMH or LIPO, if so its a really good starting point, what is the mah rating its usually a number in the 1000's written all over the battery ?
In an ideal situation you would have two circuits, one is the 5V logic circuit, the other is a power circuit which in the case of servos can be 4.8 to 6 volts - don't try and power the Servos directly from the 7.4 it could damage them.
Looking at the Ardumotor, it takes the motor power from the VIN of the Arduino, this is before the Arduino on board regulator so is not current limited by the regulator. The Ardumotor take logic power for the onboard circuits from the Arduino 5V, this is after the regulator so not going to deliver the amps you need for the Servos.
The voltage coming from vin will be too high for the servos so dont use this directly.
One quick solution is to pick up a regulator of the type used in RC Models, these are able to deliver 5 or 6 volts from a 7.4 volt battery and will also give you 2 amps or more for your servos.
This will allow you to use a single high capacity NIMH or LIPO to drive your project, connect the servos to the battery through the regulator suggested above and keep everything else as you currently have it.