No, it is not possible to run a furnace without having a filter. Furnaces require filters in order to function properly and keep allergens and other contaminants from entering the home. Furnace filters also help improve the air quality in your home. If you do not have a filter installed in your furnace, it is likely that the furnace will not work properly and could even cause damage to the furnace. It is important to install a quality filter in your furnace and to replace it regularly in order to keep your home's air quality high and your furnace working properly.