Rowling is on record as approving of HP-based fan works in general [BBC interview], but that does not mean she approves of HPMOR specifically. I think there are strong circumstantial reasons to believe that she has not and will not read HPMOR, and would not comment on it if she had.
The statement Rowling's spokespeople made in the above-linked article — she is flattered that people are inspired by her work to write their own fiction, but keep it noncommercial and age-appropriate, and make sure to credit her with the original idea — is similar to statements made by several other genre authors, e.g. Leah Cutter, Jim Hines, Charlie Stross, and see Fanlore for more. Those statements frequently include an additional caveat:
Do not ever, ever ask me to read it. [Cutter]
Please don’t ask me to read it or tell me about it. [Hines]
This doesn’t mean I want to read your stories about my characters. [Stross]
Stross goes into some detail about his reasons:
- Life's too short. (I have a multi-year backlog of reading; I do not read fast: and the fact of your having written fanfic about my characters is not, in and of itself, sufficient to give you a priority claim on my attention.)
- In any case, I have a surplus of Charlie Stross character fanfic of my own to write, KTHX.
- There is the perpetual paranoid author's worry that $FAN will show $AUTHOR a neat idea, $AUTHOR will write a book with the idea in it, and $FAN will sue $AUTHOR for plagiarism. It's about as likely as being hit by lightning, twice, but — no thanks. (Something similar has happened to J. K. Rowling and Dan Brown. I can happily live without lawsuits.)
I haven't seen Rowling specifically saying this, but Stross's third point in particular seems quite likely to apply; the "something similar" that he mentions regarding her isn't a case of fanfic leading to plagiarism lawsuits, but still, one would expect her to be avoiding anything that could lead to more legal headaches.