Planter Faciitis is a common overuse injury lots of runners get as well. Anytime you are using/overusing muscles in a way your body is unaccustomed to it can cause problems. Still, problems caused by exercise, usually have simple solutions, like easing up a little or adding a different exercise to compensate. Overall your risks of health problems are far greater from lack of exercise than from an overuse injury.
I say if you are interested in a standing desk, try it out, but have a backup sitting station as your body gets accustomed to it's newly used muscles.