Hi Nyssa,
sounds a bit tricky, but really, do they ask so much about the background of the sponsor? It doesn't seem so to me...
I'm just an applicant like you, not a consultant or specialist or anything but I have been reading these forums and the CIC docs for months now and my impression is that the focus is on mainly on you and that your marriage is genuine, and the criteria for the sponsor are not tough at all, from what I can see!
Once they approve the sponsor then I think they are only looking to see if YOU are a good candidate to move to Canada, a potential trouble-maker or whatever, and also for proof of the relationship. So if you've got a clean criminal record and you are legally married and have some good evidence of you relationship (and reading these forums many people seem to suceed in proving this even when they don't live together and just visit/phone, so already you have that advantage!) even if you cannot easily prove you lived together, that doesn't mean you're not a legit married couple.
I have no idea what the consequences would be of a rejected application but if you asked my opinion, I think you should just try and see! I've been living outside Canada and I didn't have to provide much in terms of proof of income for the past year, I do have a job waiting in Canada so that shows I can support us and that we plan to resettle, so that might have helped me...
I guess if you write a good explanation that his problem with immigration was through a mistake made when he was young, and so he couldn't be there legally, but that he never committed any other crime and he worked to support himself - So what if he went by different names? He was doing it in order to work, not to collect welfare right? But still, why would that even come up? They don't ask for that much detail of the sponsor's background actually, just the past year's income and my plans to resettle... there was not a lot to show in that respect, it was more about the proof of relationship.
Now my memory is a bit hazy but I recall when we were paying our fees for the application that there was an option to select that we could be refunded if the decision was "sponsor not approved", so that way we would go no further and get almost all the money back right up front... but I remember there were some consequences to this approach, just don't remember what they were. Maybe no right to appeal, just have to redo the application or something... Since money seems to be an issue maybe this is something for you to check into?
Once again I'm no expert at all but this is just the feeling I have reading so many stories and filling in the forms myself.
Well good luck and keep us posted on what you decide to do and how it goes!
TLH