It really depends what you have and how it is setup.
As was already mentioned you don't want to suck a vacume on the wood burner that would cause carbon monoxide to enter the home!
Really though if you have a good setup you can do anything you want within reason.
For instance, if your woodburners intake is on the front and exhaust on the rear, you could build a box around it that does not effect intake or exhaust, then blow or suck air through that box as you want. This assumes you have a solid wood burner, not one built in pieces like those cheap cast iron stoves. In this case your "box" would be around the top, bottom, sides, the stove front and rear exposed outside the box. Ok for a solid steel burner.
If the wood burner is in a large room that gets hot and you just circulate that hot air elsewhere you can do it either way, blow or suck. Again make sure your not going to make a vacume on the wood burner though.
Best is to seal the burner with a duct to draw in air from outside and preheat that air using the flue exhaust. This way the wood burning fumes are basically sealed from the house, provided you have a well sealed door for loading the wood, or load wood from outside the house.
I saw a neat setup where the hot burner case was in the house, the loading door, flue, and intake were outside the house. This was a fancy large burner that only needed loaded once a day and temps rarely fell below 5F in that area. It was a rock or brick wall so no risk of fire though!!
If done right you can even build a box in the duct work itself dending on your home and burner. In this case the normal furnace should work as normal, heat's and blows the air around the house as needed. The cold air return feeds to the box at the wood burner, if a fire is burning then hot air is fed to the furnace and less normal heating is needed. If no wood fire then the normal furnace works as normal.
So many things can be done depending what you have and want to do with it. ALWAYS make certain no fumes from inside the wood burner can enter the air going to the house!!!