Yes, to explain that let’s take a system consisting of two blocks where one is resting on the another.

Now, when a force F is applied on block B in the forward direction as shown in the above figure, block A moves with block B in the direction of the applied force. The frictional force on block A and the displacement will be in the direction of motion. Therefore, by considering the force in applied on the system of two blocks, work done by the frictional force is positive. In this case Block A will remain unmoved on the Block B. This shows that static friction is doing a non-zero work on the object.