Definitely. I have done that and created the initial backup with the external drive connected to the local LAN at the source. I am using the free Crashplan (no cloud) service. Then only the incremental updates need to go via the internet, and the transfers are compressed when possible. As for running 24/7, it will mention in the log that it couldn't connect, and will continue when the target comes online. You can set up a schedule if you wish but not necessary.

That's right. But I figure the chances of Crashplan going out of business at the same time that I need to restore from my Crashplan backup are low. Especially as my Crashplan installation at a neighbors is a secondary plan in case the house burns down or all my stuff is stolen.