I have usually called this an external seal. The flexible element (which could be single spring, multiple spring or bellows) is outside of the stuffing box. This places the pumped product on the inside diameter of the seal. This creates a couple of potential problems. If there are solids in the pumped product, they can pack up the inside of the seal as a result of centrifugal force. For many pusher seals, this would require that the dynamic o-ring moves toward the process as the seal wears. This can result in hang-up of the seal as the o-ring tries to move onto a dirty surface. If the seal rotary head is truly external, it may need to be protected from environmental damage, corrosion or contaminants. The seal faces will have to be designed for a pressure balance with ID pressure. But, this should not be a problem as long as the seal manufacturer knows how you are planning to install the seal. Our plant has about 1600 pumps with mechanical seals. I can't think of a single one that has this arrangement. But, I can't say that it is a bad idea for all possible applications.
Johnny Pellin