Value of digital potentiometer when not powered
I think the circuit has a chicken-and-egg kind of issue. The pot needs supplies to operate, but supply also needs pot to operate.
The digital resistor state is random when supply is less than 1.8V and it won't be within specs of the datasheet.
However if supply is below that, like 0V, the analog muxes that connect the wiper cannot turn on at all, so resistance would be quite high, as in disconnected.
And on a side note, all the pot pins must be within 0.3V of supply voltages, so with 0V supply, the protection diodes start to conduct at about 0.3V on the wiper pin and backfeed current to pot supply.
And the powerswitch would see the high current limit resistance and would have quite a low current limit, so it might turn off when starting up.