The indoor temp will roughly track the average outdoor temp if left unheated for a few days, somewhat higher due to passive solar gains through the windows. It'll take a few days to get there too, due to the thermal mass of the house and it's contents. As long as all the plumbing is inside the insulation boundary & air-tightness boundary it shouldn't be a problem as long as the AVERAGE daily temp is above 25F or so. Even north facing low-E windows will have some amount of solar gain, even on cloudy days, though it's east and west facing windows that will have the highest direct gains this time of year on sunny days.
Basements with un-insulated slabs will usually stay above freezing as long as they don't leak much air. It'll be even warmer if the foundation walls are insulated.
If it's an air-leaky house and it's windy, and there is plumbing is in an exterior wall it could be a problem.
Plug your ZIP code into a
Weatherspark.com dashboard, and eyeball the average temperature expected over the next day or three using the cursors. If it's below 25F for an average temperature, drain the potable water systems on the above-grade levels at least. The basement will be just fine if the foundation is insulated or doesn't have a lot of above-grade exposed foundation. Seal any clothes dryer vents etc. to minimize air-infiltration until the power & heat come back on.