No.
Unless someone with more experience says otherwise.
I wouldn't take it from PHD candidate and he or she should know enough to say so, like GellaBella said. I nearly asked for a letter from a fellow at the hospital and he said something along the lines "ask someone who will hold some weight".
As a compromise, you might try to see if the PHD student would be okay writing a letter for the professor to sign. Again, from my experience, one of my letters came from secretary signed by MD.
I've also written several letters for volunteers at my office for my boss to sign. Heck, he doesn't even sign them, I have his signature electronically. I read it out over the phone for him and he "okays" it for his signature.