will installing a ceiling fan below recessed lights cause strobe effect
Yes, it can. If the lights are directly above the fan blades (not likely for recessed lights, but a surety on a fan with uplighting), you will have a stroboscopic effect all of the time and it will be the most pronounced. It will be more pronounced when the fan is spinning on lower speeds than higher speeds. The  farther the lights are situated away from the fan, the more the effect will be diminished, possibly to the point of not being noticeable at all.