Much as I dislike Cath running her own rape kit rather than going to the crime lab for it, it is totally in her character. When she wanted to find out if Sam was her father, she didn't go about it in a professional matter. She went about it in a personal matter.
Sometimes, when stressed, Catherine doesn't make right choices. This one may come back to bite her, it may not, but it makes perfect sense for her to want to know, even if it can't help her in court. Catherine has an ache for the truth when it comes to her life since so much of it was filled with lies. After all she has been through, she wants the facts, which might be part of what led her to enjoy a life as a CSI so much.
In short, I don't think Cath has any intentions of giving her evidence over to the lab (because it won't be admissable in court, anyways) or attempting to use it later. It's just for her, in my opinion.