Should I circulate solid fuel stove heated air through my ducts?

Why does this idea come up at all? The answer is that a novice has no way to compare what a btu is with the amount of air that is needed; many installers don't know that as well. Thus heat is heat, whether there is enough sent around through ducts or not. Heat in air is magic until examined scientifically.

Will you be satisfied with only 1/5th the heat?
The idea is to heat the rooms at the other end of the ductwork. In order to do that in the winter when you use the most fuel, the furnace heats air from say 70F to 120F, a 50 degree rise in temperature. The amount of air sent to the rooms is based upon having that air heated up 50 degrees. But with a wood stove as the source, you aren't going to like being in a room at 120F to start the air going in the returns the same as a furnace would put out.

You probably are going to find heating the room with the stove in it up to 78F makes it a bit uncomfortable. This 78F air has one-fifith the heat content of the air at 120F, so you would be providing only one-fifth the heat out the other end of the ducts. You can't make the ducts and blowers larger to flow five times the heated air when the air through the ducts is 78F. You won't like the really cold air at the floor in the rooms at the end of the ducts coming back to the furnace return.

Can you make your wood stove give off as much heat as your furnace?
If you can only make it provide half as much, then you will only be able to heat the house half as much with the wood stove, even if you could move five times the amount of air through the ducts.

This places the ductwork in the attic in most ranch homes, others have it in a crawl. The ducts are usually inadequately sealed, so exchange air and are poorly insulated with less than two inches of insulation. Building codes don't allow less than 3-1/2 inches of insulation in the walls anymore, so there is not good reason to have less around ducts. A furnace supplies heat at 120F so the TD is 120-70F air or 50F, which is the same temperature difference as the heat need in your area. The installers there need to be asked that question, why install 3-1/2 inches of fiberglass insulation in walls and not around ducts.

I bring this up because you will be circulating not 120F furnace air, but 74F air from the pellet stove room, this is much less heat, so actually if your ducts are in the attic or crawl, you will lose heat from them, not gain it, so cold air will come out of the registers. In addition, if you have unsealed ducts, they will throw heated air from the home outside through the joint cracks and draw moist air in from the outside. It is also possible the colder ducts in the coldest weather can condense water inside them adding to the potential mold problem. See: Why is there dripping from my ducts in the winter?

It is better to use the furnace in the winter with the warmer furnace heater air than to waste heat and have a potential mold problem by circulating heat from the pellet stove through the leaky ducts - unless you seal and insulate the ducts to a useful level. Even then it wouldn't be as good as using the furnace.