Yes, I think you would be charged for those hours.

If you need a server up 24/7 then EC2 is not the right provider for you; you should be looking at a more conventional hosting companies (Linode and Slicehost have already been mentioned here). EC2 is for people who expect they will need an extra server (or two, or ten) up for one (or two, or ten) hours out of every week, and for the rest of the week they don't care if that server is effectively turned off.