Choosing a Hanging Cheek for the cheekpiece of your Snaffle means:
You fasten the cheek of your Bridle into the top staple of the cheek, meaning some of the weight of the bit is taken from the inside of the Horses mouth and onto the headpiece of the Bridle
The cheek of the bit is stabilised against the Horses face, and the mouthpiece stays central across the Horses tongue [its easier for a Horse to roll the mouthpiece up and down in especially a Loose Ring Cheek]
So when rein pressure is applied and then released the bit returns to the same place in the Horses mouth because of the cheek attachment.
The rein attaches to the larger ring and as the riders hands sit above the Horses mouth the rein rides in the top quadrant of the rein ring with the rein riding here there is no poll action, to create poll pressure you would have to anchor the rein down at the bottom of the rein Ring so that the cheek of the bit turns and that would create poll pressure .
An excellent cheek if you have a multi tasking Horse doing everything in one snaffle as it has a very supportive "stemmy" cheek against the Face that holds the mouthpiece neatly and centrally inside the mouth
The only time this would work against this theory if you have chosen a mouthpiece that your Horse does not like as there is less escape from the pressure with a Hanging Cheek than an Eggbutt or a Loose Ring cheek would afford
Having two sizes of Hanging Cheekpieces in your range is a bonus for fitting Small faces at one end of the scale and large faces at the other