As it is a step down converter it will perform the voltage conversion with a certain efficiency which is dependent on the input voltage (among other things). A general rule of thumb is that the with an increased voltage difference your efficiency will decrease.
So for example if you step-down from 12V to 5V you will have an efficiency of 85%, if you step-down from 45V to 5V it will be 70% (those are not real numbers, just some values thrown in, the drop in efficiency will probably be much smaller for a decent design).
Leaving that effect aside for a moment, you will increase the runtime if you put another battery in series to your existing ones. Basically you increase the amount of energy available. The energy is transferred to the output with said efficiency. So you have 7.4V and (just guessing) 2000mAh at the input, that is 14.8Wh with 80% efficiency you will have roughly 12Wh at the output.
If you put another battery in series the voltage will increase to 11.1V, the capacity will stay at 2000mAh, but the energy is now 22.2Wh and with the reduced efficiency (75%) roughly 16.5Wh at the output. So you increased the energy available to your Raspberry and it will run longer.
That said to increase the runtime, it would be better to put another battery in parallel, it would increase the capacity but not the voltage, so the efficiency will stay at the value. So instead of 7.4V with 2000mAh you could use a second pack and get 7.4V with 4000mAh, doubling the energy and runtime.
A note on buck-boost topologies: the efficiency can be very different in the different modes of operation, to get best efficiencies you better stay out of boost region of operation and just in the buck mode. (So the input should always be larger than the output, a 7.4V pack is fine in that regard)
A note on battery packs: connecting lithium batteries in series requires balanced charging or they will fail prematurely (they start to drift apart and one cell will get damaged).
Connecting batteries in parallel should have every cell connected in parallel not just the packs (so each cell can balance itself with the partners).
It is recommended to use cells of the same type to build a pack.
A note on rechargeable batteries: do not overdischarge them, implement some kind of low battery cut-off.