Long ago and far away, I had a water softener. It was run by a clock motor that turned cams to operate all the valves for the different functions in regeneration. If the house water was shut off, when it was time, the motor would run the program to operate all the valves, but since there was no water flow possible because the water was shut off, nothing would really happen, the regeneration would not occur. So no damage or anything like that.
That sounds like the only potential problem with nwsteve's situation. If this happens, the salt won't hurt the resin bed (since the brine water goes through it every regen cycle), but it might not be very good for the appliances (including the water heater). Nwsteve, it might be worth flushing out the resin bed by running a hose or the kitchen sink for 30 minutes or so when you get home (before anyone draws hot water), especially if a taste of the water indicates it has a lot of salt in it. If your WS is like mine it regenerates based on usage but also automatically regenerates every 14 days even if usage is low/nil.I did it once. No damage, but the residual water pressure was enough to get some salt into the resin bed when the softener regen'ed. Or perhaps the valve did not close completely and there was a tiny leak.
I realized what happened when I came back after the trip, took a shower, and thought somehow my head hair got a lot of salt into it from the ocean. Tasted the water and found that it was salty.