A TB+ culture is a test that is 100% positive, it shows that you have active TB -- and it's done from phleghm, so if a culture was performed, then you are able to produce phlegm. If you had a TB culture performed, then you must have either had some symptoms, or a suspicious X-ray; if you weren't producing phlegm, then they must have done a somewhat invasive test that makes you cough it up.
As for how immigration will consider this, I suspect they will take it very seriously -- a few years ago immigration was actually sued by a woman who married a Caribbean man who had drug-resistant TB. EVen though he infected several Canadians and got free medical treatment, he argued that his health was compromised by thinking that he was healthy and not getting treatment.
I don't know how CIC will consider regular TB, but I am sure they will require you to have more than 2 weeks treatment. Even though you aren't infectious at that point, you will still have to be treated for another 6-9 months, and if you quit before that period you can become infectious again. Neither is it certain that the TB will be cured, it might be resistant to treatment.
I'm sorry to be negative, I know that this must be a terrible blow; it might also be that I'm more pessimistic about CIC's view of this than is necessary.