Possible but not probable. Beside the fact that the average 5 day fertile time in a woman's cycle (and that's taking the average life of a sperm into account) is midcycle, and the fact that menstrual blood is fairly toxic to sperm, as is the highly alkaline environment during menstruation, changes are possible, but not probable. The problem comes in when women don't realize that "active menstruation" has ceased and the light blood they are seeing is left over, and the actual "menstrual period" is over and they also have short menstrual months (meaning usually less than 28 day or very erratic ovulation) that pregnancy happens during menstruation.
One needs to know one's body well. Natural Family Planning did NOT work for us, NFP is very different than "rhythm" (which is no more than counting days) I got pregnant several times during my "safe time." However, I have never gotten pregnant during menstruation. I have long menstrual cycles, very alkaline menstural fluid and even though it works for us, it will not work for everyone. Also, when one is using Natural Family Planning, menstruation is NOT a "safe time" because one cannot determine the consistency of the mucous properly, so sex during menstruation is prohibited if one is using NFP.
(Of course, using NFP to the letter, with no barrier back up, MOST of the time is "unsafe time." I honestly think the people who thought up NFP wanted people to have little sex, and may have even planned it to fail so that pregnancies happened. This is from knowing leaders of "The Couple to Couple League" and their attitudes toward sex, plus the fact that so many people I know who used it got pregnant anyway. One CtC League leader told me, when I said we were using a barrier method during most of my "unsafe times" because my cycles were so long, we'd have to go weeks without sex if barrier methods were not used. She said that my husband and I were not patient people, that we had no "self control" and were giving in to "base instincts and lust." Uh, yeah, that's why we were having sex in the first place.