Does the dihedral effect happen during coordinated flight?
No.

The dihedral effect depends on a flow asymmetry between left and right wing. Coordinated flight means that both wings have the same flow conditions, and the only asymmetry between both is caused by control deflections.

You do have a flow asymmetry during a turn (coordinated or not) from the speed difference between the inner and the outer wing which grows with the turn rate and wing span. This does indeed cause more lift on the outer wing, but due to the difference in dynamic pressure, not due to dihedral. Since dihedral causes a side force component of lift, you can argue that the outer wing creates more side force which pushes the plane into the turn. But the pilot will compensate the difference in dynamic pressure with the ailerons to stop any rolling motion once the desired turn rate is stabilized. This will also equal the lift on both wings.

Another asymmetry is caused by the location of the vertical tail aft of the center of gravity. Essentially, the tail swings around during the turn, which causes a sideslip condition at the vertical tail. The result is a side force which grows with turn rate and tail lever arm, and due to the high location of most vertical tails also causes a small rolling moment. But again the wing's dihedral has nothing to do with that.

Dihedral only comes into play if you build up a sideslip, and then the turn is not coordinated any longer. @Zeus is right with his point that dihedral stabilizes the aircraft and makes it easier to keep the turn a coordinated one. Now we can split hairs all day if flying in turbulence makes a perfectly coordinated turn impossible. When it comes to dynamic stability, a moderate dihedral effect is highly recommended.