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Yes, she will be able to be bred, have puppies and nurse them with no difficulty. The hernia repair is pretty straightforward - it is just where the muscles didn't close together where her umbilical cord was. They will make a skin incision and then close the muscles together and prevent anything from coming out of that area that shouldn't! That is all there is to fixing this and she can have a safe pregnancy. I would, however, wait until her second heat cycle to breed her.
If the umbilical hernia is repaired by a reputable veterinarian, who knows in advance that your dog is going to be pregnant in her future, I would not hesitate to breed her. You can prepare the edges of the muscle tissue in a way that it actually grows together and you can use suture that is not reabsorbable and will stay in there.
I would compare what you are reading online to what you would read about any medicine you take. If you look at it online, read all the side effects, you would flush it down the toilet. I'm not saying there is no chance an abdominal tear would happen, but it is very unlikely if the vet knows your plans, and you wait 6 months or more before breeding her.