It wouldn't make any difference either way as long as:
- it doesn't impair your discussion of the case with the interviewer (i.e. don't stare at the piece of paper the whole time)
- you are able to articulate your thinking (i.e. have sufficient structure and illustrations to make your proposals clear)
As you can see, the first point can be used to argue against taking notes, the second point can be used to argue in favour of taking notes.
There may be aspects to the case on the day which point you towards one approach. For example, in some cases you are given a written copy of all the information anyway. In other cases, you will only be given information verbally and unless you write it down it will look like you aren't paying attention.
Similarly, in numerically-heavy cases which ask for extensive calculation, or those where you are asked to make a stand-up presentation of your findings, it would be sensible to build your written evidence as you go along.