Do I need orthotics in my cycling shoes?

Yes - especially if you are competitive or do extensive mileage each week.  Experience has shown us that when the orthotics places the bones of the foot in a more corrected and structurally aligned position, this necessitates less energy expenditure by the muscles of the foot and leg as the bones of the foot lock together and in essence, stay aligned during the thousands of "up and down pistoning motions" while cycling.  Conversely, when the foot is not in its ideal structural position, it necessitates the muscles of the foot and lower leg to work harder to keep nudging the bones of the foot back into their ideal alignment.  This done over and over during the hours and thousands of down strokes of the cycling action, causes the muscles to work much harder and predisposes them and even the bones of the foot to injury from overuse.  
Almost one for one, the cyclists who use these types of orthotics in their cycling shoes have relayed they go faster and longer using less energy and experiencing significantly less "fatigue" during cycling.  Depending on the style of cycle shoe, you may necessitate a pair specifically for that activity but for the most part, the orthotics that you can put into your sneakers or lace up dress shoes fit into cycling shoes.