No, it does affect the integration a bit, this is why: There is an amount of light entering the sphere. Because of the baffle it can not directly illuminate the detector but light that has undergone a first reflection can. This first reflected light comes, depending on beam shape, from all sides to the detector or from a certain area in the sphere, so the angle from which it enters the detector is not random and the distance from which it comes is not average. So the reading of the first reflection is susceptible to limitations of the detector. Light that has undergone more than 1 reflection probably already is random in distance and angle from the detector. Now, the better the reflectivity, the higher the contribution of multiple reflected light to the lux-reading, and that is lowering the contribution of that first reflection of which the reading can not be fully trusted. (in case of 90% reflectivity of the combined inner surface of the sphere, which is already a challenging number for non-professional coatings and the presence of holes that fit flashlights, a quick and dirty calculation learns that light that has been reflected once contributes to about 11% of the light that reaches the detector, probably in reality this number is higher).
That is of course a quite qualitative test but it does give a good indication I guess. You do not know how many reflections the light that comes through the walls of the sphere have undergone compared to light that is bounced inside the sphere, but you do know for sure that unlike the light inside the sphere there is no contribution to the reading of the first couple (10? 20? I don't know how many reflections it takes to get through 2cm of styrofoam) of reflections.