Power at VBAT versus BAT_IN

So just to be sure, we're talking about the 2x 0.1" pins, BAT_IN and VBAT as shown on: https://www.espruino.com/Pico#pinout

For those:

• BAT_IN is the one you should connect batteries too (it's also connected to the JST connector footprint that's on the rear of the board)
  
• VBAT is what's actually marked as 5V in this schematic: https://www.espruino.com/Pico#-a-name-power-a-power-and-the-fet-b0-jumper
  
  

When I have no USB connection, but have 4 x AAA rechargeable batteries (~4.8V, ~600 mA) connected to GND and BAT_IN, will I see full power (voltage x current) at the VBAT pin

You'll see full voltage, but power goes through the FET so it's not 'full current' - but it should easily handle 1A which sounds like it's fine for you.

When USB is connected you'll see USB volts via the volt drop of a diode - and I'd avoid trying to pull any more than 500mA off that because the diode won't like it!