In reply to Trevers:
I'm going to go out on a limb and disagree with most other posters. If you are passionate enough about climbing to worry about the impact a Phud will have on it, you are more likely than most to run into problems. Not saying it's a no, but give it serious thought.
I can remember asking my supervisor at my initial interview if he saw a problem with me doing trips climbing. He said no then but when it came to having just three weeks for a Yosemite trip teeth were sucked in a big way.
He had actually done some climbing so I had expected a more sympathetic attitude to climbing trips but the bottom line is that there are climbers and climbers. Other members of the group or department may have very different interpretations of flexibility on taking holidays. For many people two weeks is a long holiday! Only you know how afflicted you are and how much time you really want to spend climbing.
I was in Southampton and frankly hated the lack of local climbing. I drove to Sheffield 4 weekends out of 5 and it knackered me out. The result was that I came to hate the place and ultimately the Phd. In the end, I never wrote up.
As someone else said, you have to realllllllly love what you're doing. Another poster said you'd have to be crazy to ask the question - to turn that on it's head, if you're asking, maybe you don't love Physics enough?
In my case, it turned out okay. I was cured of my Chemistry and now work in climbing