You can, but typically not without it being a bit of a pain to set up. The problem is that with a pull-down faucet the aerator may be difficult – if not impossible – to remove from the spray head. Some may recommend pulling the spray head off, then using different adapters to get to the quick-connect needed for the portable dishwasher’s water connection.
So yes – it can be done. And no – it’s potentially not very simple.