Have cell phones

A: Many villagers in this district have cell phones.

B: Many villagers in this district (each) have a cell phone.

I think A is the same in meaning as B, but there is something ambiguous in A.

Is it possible to interpret A in the following way?:
Many villagers in this district share multiple cell phones.

Of course the above interpretation can be ignored because it doesn't fit our common sense, I think. I just would like to know whether the interpretation is possible or not.