Questioning is generally a good modus operandi for board members, implying openness, curiosity and a willingness to listen and explore issues.
But there are two behaviours to avoid: when questioning is perceived as repetitive or pursuit of a 'hobby horse', or when others feel adequate answers have been given, back off. You risk being perceived as awkward and unhelpful. The best boards encourage collegiate working, so when questioning is obstructively persistent the chair needs to remind the questioner to respect the views of the majority of the board.
There is an equal danger that board members don't ask the difficult questions, being anxious about asking a silly question or fearful of upsetting someone. The obvious question no one dared ask can often shed new light on an issue. The chair should strongly encourage these questions and discourage the evolution of institutional politeness.
Intelligent questions, put respectfully, should always be welcome; they can help to get to the heart of the matter and play an important role in delivering effective governance. And if you are not sure, test your question on someone else before the meeting.