I was observing how the A-Star board is behaving. And it really does that, if SHDN is not connected it draws more power than SHDN connected to the BAT+ terminal (within 2.2 to 4.4 range).
I also measured the buck output voltage from the 5V terminal. If SHDN is not connected the voltage is roughly the same as the input voltage, in the range 0.5 volts up to 5 volts. If SHDN is tied with the BAT+ to the lab supply, the 5V output stays at 0.5 volts all the time I raise the voltage up from zero. The 0.5 volts is just a residual charge at board bypass capacitors.
This is of course not a huge deal. In normal use the board powers up just fine, the BOD prevents any misbehavior with insufficient input voltage.
I'm trying to do a batteryless system with some energy harvesting system charging a capacitor and when there is enough voltage the board should power up. Goal is to minimize the power draw while the board should be off. I could also use external fet to cut off the BAT+ supply completely but first I wanted to try the SHDN input.
I have been drafting an undervoltage lockout circuit with LMC555 timer IC that should be operational from 1.5 volts up and that can either control the SHDN input or a separate mosfet. With this I have good command of power-up and power-down thresholds and SR-flipflop prevents any oscillations at startup.