Although carpet will absorb some of the sound it is better to place the down fire on carpet than it is on hard smooth surfaces as these will reflect sound directly and cause a boomy listening experience that can be fairly unpleasant.
Down firing sub carpet.
My family room is fairly small 15 x 12 and carpeted.
And even for a down facing subwoofer the amount of sound being absorbed by the carpet is likely going to be negligible.
And since the shaking directly affects the floor the floor starts shaking.
A down firing subwoofer box produces a domino effect if placed inside a room.
Is it worth the time to cut out a small 13 x 13 piece of plywood to sit the subwoofer on to increase bass rather than just have it sitting directly on the carpet.
I just ordered a pswi 225 down firing wireless sub.
You also have to leave 1 4 to 1 3 of the cones diameter for clearance other wise you will run into cancellation issues.
Keep doing that until you have 3 4 options so you can narrow down the big winner.
I have recently built a center console for a f 350 with 4 8 focal utopia be subs firing down with slot ports firing forward into the dash.
Most down firing subwoofers are placed on softer surfaces such as carpet.
Put a piece of tape down on the floor when you notice things are sounding good then move to another spot.
The domino effect starts because of the shaking of the subwoofer box.
I have a downword firing 12 inch ksw klipsch sub i now wish i had been smarter and done my homework and bought a better sub for the price anyway on the klipsch forums several posters suggested that if you have carpet like i do to put a large ceramic tile underneath the sub.