Yes. You can define a special-relativistic momentum and it's a conserved quantity, and it does have a nonzero value even for things with zero rest mass (which necessarily move at the speed of light).
(It may help to observe that an object with nonzero mass moving at the speed of light would have infinite momentum, and then it maybe makes sense that "zero times infinity" becomes a finite number)
Comments
Yes. You can define a special-relativistic momentum and it's a conserved quantity, and it does have a nonzero value even for things with zero rest mass (which necessarily move at the speed of light).
(It may help to observe that an object with nonzero mass moving at the speed of light would have infinite momentum, and then it maybe makes sense that "zero times infinity" becomes a finite number)