There are a variety of policies and procedures that different breed groups follow. Knowing our breed I think that most rescue groups try to place a dog in "foster care" so that we can get a personality evaluation on the bulldog before it is considered for placement...and experienced bully owners/rescue workers can get pretty good at this to where they will know the rescue dog well...the question often remains about the resident dog and whether it is willing to accept another dog into the family. Some potential adopters are clueless as to reading the signs of their own dog in response to another...have never "babysat" another dog or had one stay at their home to observe their dog's responses and interactions with a new animal.
There are several factors that would govern a situation that was described above...and there are many "unknowns" here including but not limited to the personality of the rescue dog, the resident dog, the potential adopter's experience with animals (multi-dog home) and the experience of the rescue group's volunteers in evaluating the entire situation. I strongly feel that there should be a "home trial period" for any adoption and that it is the responsibility of the rescue organization to provide as full a picture of the rescue dog as possible including behavior, health and history for the potential home.