Yes gas fireplaces can run continuously when needed to maintain temperature in a house especially during a power outage when you have no other heat source.
I run my gas fireplace a lot continuously when I'd rather just heat the small area where I'm at to a good temperature and leave my gas furnace off.
The gas fireplace is much cheaper to operate than the gas furnace so I try to leave the furnace set a lower temperature when I can to save money.
But I let the furnace to the most heating especially at night or when I'm using other rooms in the house.
But there's no problem with letting the gas fireplace run all the time.