The simple answer is: maybe.
The standard tripod or quadrupod grip that every occupational therapist teaches will give your child a solid, controlled hold on a pencil for handwriting. Most children can learn this grip by 4 years of age. Some children watch adults and seem to copy it effortlessly. What happens to the rest of them?
Some children end up using a pencil grip in kindergarten, and I strongly prefer to wait on recommending this choice until I have seen that hand exercises and activities have not resulted in a stable independent grasp. In highly academic kindergartens, there can be a high volume of handwriting. Allowing a child in such a class to habitually use a weak or unstable grasp is simply unfair. I prefer to support a struggling grasp with the type of pencil grip that looks, quite frankly, like the head of a cobra. The “hood” prevents fingers from rolling over the pencil or each other. This style of pencil grip requires a tripod position, and actually I consider it the only grip that creates more finger strength and control as it is used. I encourage frequent reassessment of grasp to reduce and remove the use of pencil grips as soon as possible.
Current research will support both the stance that a good grip is essential for good handwriting, and the position that it is irrelevant to legible handwriting. I see both sides. If I had a dollar for every parent that wrote me a check for services using a “hook” grasp, I would be blogging to you from Hawaii right now. Most of them have advanced degrees and no physical limitations (that I know of) save an unusual pencil grasp. If your child complains of hand and finger fatigue, or you can see that his grip is making it harder for him to write certain letters, then you have to try to change that grasp pattern. Letting a child struggle is not kind. If your child is a neat but very slow writer, then take a look at his grasp pattern and consider whether it is contributing to his speed issue. There may be other causes for slow writing speed, but it is worth exploring whether grasp is a part of the problem.
Final thought: Pencil grasp usually has to be taught. Tool use is not inborn, so model it and support your child’s efforts as they grow!