Certainly! Fingering is one of the most important factors involved in playing piano, so where the black/white keys get pressed is paramount. Particularly in the faster passages.
One might assume that key C, with all its white keys, is the easiest, but that's not always so. Often, keys with black keys will make moving along the keyboard easier, giving room for a thumb to pass more simply underneath.
EDIT: You ask about exams, and the reflection they have on certain keys. I'm somewhat dismayed to say keys are not chosen with much relationship at all, it would appear. With all the exams I put students through on guitar, the scales and arpeggios learnt for particular grades had a large connection with other parts of the exam. Actually it was that fact that really brought it home to me (even as a teacher) how useful scales could be!
But, a lot of the pieces specified for ABRSM (don't know about other boards) bear no relationship to particular keys, thus scales and arpeggios, which seems a pity - and did nothing to clarify why I (as a student) needed to learn a particular scale from a particular key.
But there are many other aspects of piano playing that are in consideration as far as exams go, and I'm sure fingering for certain pieces in the choices is one - of many, as I say.
There are players who prefer certain keys, for personal reasons. I used to play with one who really liked F♯, due to all the black keys. It's said that a certain composer would write just about everything in E♭. Reasons unknown.