Can the reaction from static friction cause motion? Let's take for example, a sphere is that is pure rolling on a block without slipping. The side of the block facing the sphere has enough friction for pure rolling, but the other side is sitting on a perfectly smooth frictionless table. Since the sphere is pure rolling, there will be static friction applied on the sphere, and hence due to Newton's third law, an equal and opposite force will be applied on the block. Will it make the block move?
 A: Yes the block will move, but only if in the first place static friction is in fact required for pure rolling of the sphere to occur. For example, a sphere already rolling on a flat horizontal surface with no external forces or torques acting on the sphere requires no friction for rolling. It will continue to roll due to its inertia.
On the other hand, if an external force or torque is applied to the sphere, static friction would be required for rolling without slipping. The force the sphere applies backwards on the block due to the applied external force or torque is the only external force acting on the block, if its other side is frictionless, thus causing the block to accelerate.
A real life example involves wedging a flat wooden board between the drive wheel of a car and ice in an attempt to get traction. Often times the result of obtaining the traction is the board is propelled in the opposite direction due to the low coefficient of static friction between the board and the ice.
Hope this helps.
A: Static friction reaction between the sphere and block is different from zero only is the sphere accelerates.
If the sphere keeps on with its motion without changing momentum and angular momentum, no external force (besides the normal reaction that equilibrates the weight) acts on it, including the static friction.
A: There is a simple demonstration of the situation you are describing: If you are on a small boat and begin to walk in one direction, the boat will move in the opposite direction. In this case friction allows you to walk, and the low friction between boat and water allows the boat to move. The motion will be such as to keep the center of mass of the boat and the walker at the same  place. That's because the force generated by the walker is internal to the system and as such it cannot cause the center of mass to move --this requires an external force.
