We assume that an object is placed on a horizontal plane. If this object is accelerated to vertical direction, will frictional force act against the vertical direction of velocity of object? For any kind of applied force, will frictional force work against the vertical direction of velocity of an object?
Let me simplify your question.
An object is placed on a table.I apply some force on the object in the vertical direction. will the frictional force between the table and the object will oppose the motion of the object in the vertical direction?
Ans is no. Frictional force will be present if there is a contact between the object and the table. if you apply a force on the object in the upward direction the object will simply move upward as the object will be no longer in contact with the table.
In physics, the normal force is always perpendicular to the surface of contact between two bodies. And when there is friction, the force of friction is always, by definition, perpendicular to the normal force. The magnitude of the friction force is also proportional to the magnitude of the normal force, and the constant of proportionality is denoted as $\mu$.
Note that the normal force and friction force are actually two perpendicular components of a more general, single "contact" force, but we split them up to make solving problems easier.
In a simple scenario involving an upright table with a flat surface, the normal force the table exerts on an object placed upon it will be vertical, at 90-degree angles with the tabletop. Friction will consequently be parallel to the tabletop. Regardless of the acceleration of the body on the table, the direction of the normal force on it from the table will always be vertical, and the direction of the force of friction will be always be some horizontal direction, depending on the motion of the body.
To answer your title: No, friction will not affect the vertical motion of the body if the body is on a horizontal plane.