Is it possible? ?

it is but keep the pigs away from the dog

I’d keep the guinea pigs in a room that the dogs aren’t allowed in, and only allow the former into other rooms when the latter is out of the house.

You can definitely have both. I'd keep the guinea pigs away from the dog and i'm sure you know that but yea you could have both. They would have to warm up to eachother then they would be ok with eachother. 

It is certainly possible I have had dogs, cats and guineas at the same time, my cat would go and lay on th lawn with them ( including the baby pigs) I have a photo somewhere of the cat sunbathing with guineas climbing all over him and the two dogs watching on .... you need to be very careful about the breed and temperament of dog you get and put the training in with the dog daily and from day one

Its very possible. Get a low prey drive dog and get them a secure cage with a lid if the don't currently have one. If the dog bothers them you can move them to a bedroom or office or any room that you can block off from the dog.