With this MOSFET driver IC, is the output voltage range 0 to Vin or 0 to Vcc?
Nope. It wouldn't work as the driver needs Vcc-0,8 before it switches.

You can use the MCP1406/07 as it is much more versatile. 

Remember when you're using a MOSFET driver, that you must place a decoupling capacitor between Vdd and GND (the MCP1407 has two Vdd pins) and a low ESR 0.1 uF electrolyt capacitor between Vdd and GND, to deliver the charge quickly. 

On the input place a pulldown resistor. 

:)