Hi Sean,
I moved to Geneva to join my husband last month and we recently got a dog from the SGPA. We had been mentally preparing for all the strict and long processes we had been told to expect when attempting to adopt a dog but we were actually able to walk out with our dog, Paulo, on the same day on a trial basis. We were very shocked!! No requirements to do the training or anything like that and no visit to our apartment to check anything out just asked us a bunch of questions at the centre and if your french is like ours, weak!, you will want to take a friend along to translate! We haven't yet gone back to do the official adoption forms for a number of circumstances getting in the way but will be doing so next weekend and don't envisage any problems at all as Paulo is very much part of our family now.
There is also a really useful document for dog owners I can forward on to you where they show all the places dogs are and aren't allowed in public spaces and where they have to be on leash etc.
The very best of luck to you and any further questions on our experience don't hesitate to ask!