Can I shut off the water to my house and safely leave the water heater on while I'm away on vacation for a week?
I would turn the water heater to pilot if you turn the water off, pilot will keep a small amount of heat there and unless it gets crazy cold would help prevent freezing. I grew up in that area and rarely will it get cold enough to freeze pipes inside the house even if you turn the heat way down, 

I never recommend turning the furnace totally off as that can cause cracking of joints if Sheetrocked. 

If you turn the water off the water heater should be on pilot or turned off.  I have replaced a few water heaters over the years that were damaged from cycling with no water.