Yes - it's almost definitely a reason. Are his fingertips especially bendy? If so, he will have problems with maintaining a good and not tiring pencil grip and with knowing where his fingers are and controlling the pencil.
Things that can help are:
Chunky triangular pens or pencils, or a pencil grip. Stabilo do shaped handwriting pens which are supposed to be good, though DS1 refuses to use his.
Hand gym - lots of ideas if you google, but the idea is to strengthen the fingers and improve coordination, so activities like moulding dough, or manipulating a small coin from palm to fingers and between his fingers.
Sometimes a writing slope can help, as this improves the positioning of the paper.
If his writing is particularly heavy, practice with a soft pencil, shading from dark to light, then writing his name as lightly as possible, so it can be rubbed out without making a mark and doesn't go through to another sheet of paper.