How long should it take to drain a home's water pipes through a faucet?
Yes, all the water will drain from the second floor. It will take awhile because the faucet you're opening probably has an aerator on it which restrict flow and you only have gravity as a flow force. When working on a one story house the pipes, for the most part, are all horizontal so gravity isn't a factor.

You can speed up the draining on two story building by opening more faucets, some on the second floor and ones without aerators. 

Don't forget, you have to drain the hot water pipes too.