No, it isn't enough to compare the original characters followed by their upper-cased versions. If the two characters being compared are İ (the Turkish uppercase dotted i) and ı (the Turkish lowercase dotless i) then you need to convert them both to uppercase (yielding İ and I) and then back to lowercase (yielding i and i) before you know they are the same except for case. Provided your default locale isn't Turkish, that is.
Have a look at this article for more about those letters:
Dotted and dotless I.