I have not found any 5 V pin on the Picocalc board in Battery mode. The usb connector on top of the board is 3.3 v.
After more testing I have found out that the stetup with the stepup converter and USB does only work if connected to charging. Sometimes even the keyboard does not come up. I think you are right about the power issue. No damage, but not enough Power from the batteries. I will try some more quality cells, but for now it should be better to use a 3.3 v wlan in the first place.
It is my fault because I have tested with the board connected to the PC with adb shell connection.
I have not tested with batteries alone.
Further testing has shown that it is only a problem on boot up. If you connect the USB Wifi after booting it is fine. It draws about 0.085 A.