Current draw vs # of radios active? (XBee 2.4GHz S1 & S2C)

We’re optimizing our firmware in a product that used XBee 2.4GHz S1 radios, and will be switching to S2C. We use DigiMesh protocol and the devices are setup as non-routing (end devices).

Some people in the company think that the current consumption (these are powered by a single AAA battery) is higher when there are more units powered on. In other words, if you test battery life for a single unit on versus 10 units on, the battery life will be longer for the single unit and the 10 units will have a much shorter battery life.

Is this likely? I haven’t tested this out yet, but I assumed since they are end devices there is no handshaking (or similar) going on that might account for this.

Thanks for any ideas that might explain (or discredit) this idea.