Essentially, yes.

William faced many challenges when he succeeded his father as Duke of Normandy, two of the biggest were his illegitimacy and his youth (He was around 7-8 years old)

For most of his reign William enjoyed the support of most of his vassals, many of them fought among themselves. William did his best to subdue them, but it was many years before he succeeded totally. By referring to him as 'William the Bastard' many legitimate nobles sought to undermine William's power.

EDIT: I should clarify, William was indeed born a bastard, but he was definitely the legitimate heir to his fathers Duchy. When I said his illegitimacy was an issue, I strictly meant the fact he was a bastard, not that he had an illegitimate claim.