Provided, Chopper eats the Devil Fruit along with the other deers, will they all have the Devil Fruit ability, given that acquiring the ability only requires a single bite?
From the One Piece wiki:
Only one bite is needed for the user to gain the power of a Devil Fruit, after which the Devil Fruit becomes a simple, useless, disgusting fruit
So I would say that the answer is no. Only one person/animal gets the ability.
When a Devil Fruit is bitten (even once), it loses its powers PERMANENTLY or until the person who bit it first dies. When the person who first bit it dies, the Devil Fruit returns to its normal state, so someone else can get the power. If Luffy died (what a sad thought!) then the Gum Gum fruit would be able to give someone else Gum Gum powers. So only one person at a time can have its power, not more than one.