I was wondering if it was dangerous for the ADUM to unpower one side? All inputs on the unpowered side are connected by a pull down resistor and will not have any signal on it.
It's allowable for power to be removed from either side of the digital isolator without causing damage. The only concern would be if an input on the unpowered side were to be driven high, which could parasitically power the part through the ESD protection diode. You've indicated that you'll have the inputs tied low so this shouldn't be a problem.
There's a table in the ADuM744x data sheet which describes how the part will behave based on the state of the input or output side power supply. Here's an excerpt for your reference: