No way do I sharpen while-you-wait. For one thing, it's almost certain that someone else will call or come in while I'm doing it. Plus, that will just spoil people. They will think they can get a walk in shapening any time they want. And then a time will come when your too busy to do it, and they get pissed. It's best to set your own boundaries and stick to them.
I think most people that want it done immediately are really more interested in not having to make a return trip to pick it up. Few of them are in any kind of urgent situation where they have to finish a job. If it's really urgent, then buy a freaking chain! Most of my chains are only $17 to $20. And if they want me to "throw it on" I charge $5.
If someone I don't know drops off a chain, they pay up front. That way, I get paid whether or not they ever come to pick it up. Chains that hang around too long get used around the shop or given away to someone who could use them.