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TPS61160A: Can this part run with VIN=3V3 and the inductor connected to a different higher supply

Part Number: TPS61160A

Hi,

Can I use a TPS61160A as shown below, with Vin=3V3 and the inductor connected to a battery (3.4 to 12V)

I think it should be more efficient when the output is a low current (which mine in), because the Iq will come from my 3V3 supply:

3V3 connection: 1.8mA x 3.3V = 5.94mW with 10% conversion loss on the 3V3 = 6.5mW

Vin connected to battery: 1.8mA x 4V = 7.3mW with no conversion loss, getting worse when the battery is fuller

Thanks

:-)