What about the bugs in the beer? What happens to the bacteria you put in the flanders to sour it (i.e. the Brett strains)? Do they die after the beer has aged long enough?
If you are adding any additional sugars or malt at bottling to carbonate the beer, then you should add fresh yeast to ensure that is what that sugar does. Once the beer is carbed, those yeast will go dormant, and any lactic or brett bugs can keep on slowly doing what they have been for the last 9 or so months.
Since brett and lactic cultures are still working on the dextrins in the beer, they will still probably be there. But even if they digest things in the beer, they might not produce gas.
If you have lactic bugs, some varieties do not produce any Co2 at all, including most dairy strains, although they will quickly consume the sugars and sour the beer further.
Even if the lactic bugs are gas producers, simple sugars are much easier for lactics to consume than the dextrins they have slowly been working on for months. The lactics will probably get to the sugar before any small amount of dormant live yeast that may present. So your beer will carbonate fairly quickly, but it will be noticeably more sour than before you bottled it.
I can't say about Brett, I don't know if it will create Co2 or not, it might depend on what type of carbohydrate they are digesting. If it is sugar, it will most likely produce gas. But again, if there are lactic bugs present, the brett will be competing with them for the sugars.
You really should be adding yeast if you are adding sugar. However, if you aren't adding sugar, the beer may still carbonate if the strains present are gas producers, as they slowly work on the dextrins, but it will take time.