What I would do in this case is to spend at least one morning at this site with only a spot meter and without the camera. I would note the changing light conditions at one minute intervals. Obviously in order to duplicate conditions, the sky must be clear. Taking a note from Les's book and also Ansel Adams as well, previsualization would serve one well in this case. From the notes that I would have made, I would be able to determine how this scene would render in a print and make my time of exposure accordingly. From this time of exposure, I would then work out the reciprocity considerations, since I have already noted the light conditions. I would use an "average weighted" exposure since to guage reciprocity on the beginning of the exposure would be inaccurate, just as guaging the exposure on the ending would also be inaccurate. One must note that the daylight is either lengthening or shortening each day depending on the season. The times of sunrise are published for most locals and dates. This would determine the relationship to actual exposure versus the test data.
To answer your question as it was posed, the film is exposing at an increasing rate because of the increase in intensity of the light conditions. If you are determining your reciprocity considerations on the light at the beginning of the exposure, you will have an overexposure. If you determine it on the light intensity at the end of the exposure, you will have an underexposure. Yes, obviously the light at the beginning of your exposure, so long as it was of sufficient intensity, would serve to break the exposure threshold of the emulsion. How much? I can't tell you precisely...obviously not as much as the later and more intense light.
Hope that this helps you. Good luck.