Does a boost converter affect the life span of the source battery?
No, not directly, the battery capacity is a property of the battery.
The boost converter is just a device that changes the voltage.

What you have to consider is POWER ! Unfortunately battery capacity is often mentioned in Amp-hour, for example 1 Ah means that the battery can deliver 1 Ampere for 1 hour. But it depends on the battery VOLTAGE how much energy that represents ! Obviously a 1 V, 1 Ah battery contains less energy than a 10 V 1 Ah battery. The first is 1 Watt-hour (1 Wh), the second 10 Wh, or 10 times as much energy.

But back to your question, note that a boost converter boosts the voltage. Suppose the output of the boost converter provides 5 V and you load it with 0.1 A, so that is:

5 V x 0.1 A = 0.5 W

Now let's assume your battery is 4 V Will it be loaded also by 0.1 A ?

4 V x 0.1 A = 0.4 W

which is less than 0.5 W, so no this is not correct !

What happens is that the power that goes into the boost converter is about the same as that which comes out (for simplicity I assume the boost converter is 100 % efficient, in practice 90% efficiency is achievable) so there is also 0.5 W going into the boost converter. So your battery is also loaded by 0.5 W so how much current is that ? 0.5 W / 4 V = 0.125 A.
Aha ! That current is higher than the current at the output of the boost converter !

So compare the situation that you draw 0.1 A at 4 V from the battery or use a boost converter and draw 0.1 A at 5 V via a boost converter.
Both cases 0.1 A BUT more power is consumed in the 5 V case.

So that decreases the battery life since you discharge it more quickly !

Battery capacity (how much energy you can extract) also depends on how you load the battery, if you do not load the battery very much you can extract more energy out of it than when you discharge it as quickly as is safe. But this is probably not the effect you were asking about.