The thing that matters is how many hrs per day the chicken experiences with the light level above some minimum (approx the amount of light it takes to be able to read a newspaper, if you want some sort of ballparkish figure). The lower that number (especially below 14), the poorer your egg production is likely to be -- although some production layers will keep poppin' the eggs out more or less irrespective of daylength, at least when they are young, and breeds differ in how badly and 'soon' their laying decreases in short days.
So having the coop in shade is not a problem per se, since it does not affect when the sun rises and sets
HOWEVER, if having the coop in a shady location means that it gets darkish (like too dark to read the paper) INSIDE THE COOP rather early, and stays that way til the sun is well up in the morning, then your birds may be percieving day length to be a lot shorter than it really is and it may shorten the fraction of the year during which they lay well. (If you've ever lived/slept in a room whose windows are deeply shaded by gloomy trees or buildings, you will know how much later you sleep in in the morning that way compared to having a well-lit window even if the sun doesn't come directly through it!)
To a considerable extent, you can compensate for a shady/dark/gloomy location by having more and larger coop windows, as long as they don't turn it into an oven during the day as the sun moves around.
My coop is inside of a run that is completely covered. However, they do free range and if not, another portion of the run is open to sunlight. I still get 12 to 18 eggs a day out of 21 hens. So, I don't think that will hinder laying. They will get some light wont they? Some one else may differ.