I know this thread is old, but thought I would share what I have this in my house since I see some posts from this month.
As long as the through floor registers are "boxed" in, to prevent fire from running down the floor joists, that is what is code here. I bought a 25'x25' 3 sided log house with gambrel style roof. The only heat source was a heat exchanger off of the hot water heater with only a discharge air downstairs. In the winter, anything cooler than 20 below, the house would barely be able to stay 60* with the upstairs staying 15* cooler than the lower floor. After only having 45* in the bedrooms upstairs I installed a BK princess. There were 3 through vents to each room upstairs, and I installed a 6" and 8" inline duct fans on a line thermostat with no help at all as a temporary thought/solution to maybe get through the first winter. It did move air, but not enough to make the noise worth listening to and wouldn't even heat the upstairs up 5* more. The round fan sitting in a square hole, doesn't seal from floor to floor, so there is a major efficiency loss. and they are noisy when there is not ducting to absorb the sound.
Since, I have sacrificed the spare room closet a bit, and installed two 6" lines off the main trunk of the heat exchanger, and installed a second thermostat upstairs that only turns the fan on, when it "calls for heat" that discharges into each room and the hallway. If I am going to be gone from the house more than 3 days, I'll turn my water valve on, and have the normal house heat work while I am gone. Having a concrete pad heated by the wood stove, holds a tremendous amount of heat, but heating it with the h20/exchanger never would be warm at all. Now the upstairs is within 5* difference than downstairs, and in the winter I run the wood stove 99.9% of the time. I have blocked the discharge downstairs to allow more of the air to be forced upstairs, and the return air comes through the floor vents now and the stairwell. Since there is decent airflow now, the upstairs thermostat kicks the fan on maybe 3 to 4 times a day, for about 10 minutes. Before I found that a box fan at the bottom and top of the stairwell to be most efficient.
It is completely legal, as long as the floor is boxed in, where there is no air gap. From my experience, there isn't much air transfer as one would think. Also, one last input, anyone who has a stove that isn't using a fresh air intake, should consider spending the $50-100 for the adapter plate and piping, and use that! I saw a huge difference in how my house behaved to my stove! The windows and door jams stay dry and have no frost built up from sucking in all the cold air. I know some new homes require the kit because they are too tight and won't even create a draft. Hope that this can help someone.