I thought you could get your CFA done early as long as your instructor holds on to the scores and submits it. The CFA stuff I have says that he/she can do it electronically.
Unofficially yes, officially you will have to ask the admissions office.
If I was your CFA tester, I won't be comfortable with giving you the test now and reporting the score later without something from the admissions office saying it is okay. But that's me.