Looking at your example first let's assume that what you mean by 'approximation' in your title question is to have some knowledge for the solution but not the full solution (which comes either by means of approximation or other means).
So, yes, having some knowledge about the solution does help us find the exact answer. Here is how and why using your example.
Knowing nothing about the solution would have us as you say look at all 100 elements to count 1's. But knowing that the 1's are either 50, 51 or 52 in the case of 52 we do not have to read all 100 elements, we can stop at the 52nd 1 found without checking any further elements. This helps us because it improves our overall average complexity to reading 92.32 elements instead of 100.
So, in conclusion, while having some knowledge about the solution does not provide any help using worst case complexities (i.e. considering the worst input case scenario) it does provide help generally i.e. when considering each input as likely or in the average case.