Here is my opinion.
My last female to have a litter ran 2 days before she gave birth. She did not run with the other dogs long but she ran. Two negatinves I can think of are scratching her underside and weight. You have to keep her wieght on her. The puppies were fine but I will not do it that late again. I now relize raising pups is a stress on the female and she needs to be well rested.
I now have a female that has been carring pups for 3 weeks. I will allow her to run once a week for the next three weeks then put her up. I just want her to get some exercise and she hates to be left in the pen listing to the race.
That is just my opinion it an 75 cents will get you a coke.
I think it does good to run the female while she is bred it will help keep her in good shape for when th pups arrive. I would probobly quit around 6 or 7 weeks though to give any scratches she may have time to heel up before pups start trying to nurse