you can install a service pack with SQL either up or down. If it is down when you start it will be down when the SP completes. You will then have to start SQL and it will run through upgrade script mode.

If it is up when you start the patch will bring SQL up as the last step, running upgrade script mode as it does so.

how long it will take will depend on power of server, no of databases and whether the patch exe is local or across a network, but about 10-15 mins.