Depending on the rate of the drip, it may not help.  In the winter months, when gone for even a few days, I usually turn the water off at the meter then open the valves i.e. sinks, tubs on all levels, and flush the toilets.  In the event of furnace failure, it will not prevent all frozen/burst pipes, but you will know quickly enough of such failure when the water is eventually turned on.  The damage will be then be very local.  For longer term absence, 'blowing' the pipes and plumbing antifreeze in the toilets is suggested.