Can I use an air gap faucet as a standard faucet?
I think the air gap in an air gap faucet is separate, mechanically speaking, from the actual faucet. It's just in the same mechanism because both need to be in a similar physical location. Leaving both the drain and waste lines disconnected should be appropriate, and shouldn't give you any surprises.

To expand on that:

The air gap in a RO system exists because it needs to flush itself with water to clean up every so often. That water is waste water, and is not drinking quality. So, it goes down the drain. The air gap has the same purpose as on a dishwasher; to ensure that any blockages result in water overflowing into the sink instead of backing up or damaging any equipment. (Note the overflow hole in the faucet.) Because this mechanism relies on gravity, it needs to be placed above the level of the drain. None of this interacts with the actual faucet, but the faucet also goes next to the sink, so you might as well reuse the hole. You could have a dishwasher-style air gap and a regular faucet, and that would also work.