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Maybe, depends on the seriousness of the lates and what the rest of your profile looks like. Would really need more information and there is not enough to make an educated guess with just this. Doesn't really matter, any baddies gone is a good thing and will help your score over time if not right now. This is definitely a marthon and improvements are not always seen immediately after a change.
The collections are going to continue to drag on your scores, expecsially ones like the mortgage numbers as they are very senstive to collecitons even if they are paid and under a 100 bucks.
If any of your collections are updating, I doubt it very much.
When you have collections, your payment history is far from 100%. They may not be associated with lates on revolving credit or loans, but they are just as bad if not worse than lates.
With those collections still on your CR, I would not expect to see much gain from SL lates going poof.
Big gains are seen after last derog is gone. Reducing utilization below 29% may result in gain, but not to the tune of 60 points.