No I don't think it's the size of the family as much as the morals and the social behaviour of the family that the child is exposed to. If the large family is hostile and tend to leave issues unresolved then the child is more likely to become a bully. If relationships are detached in the family, and interactions are relatively cold then the child also is more likely to become bullies.
In a way, the larger the family, the more of these sort of things occur (detached interactions, unresolved issues, etc...) So, in a way, that may be true. On the other hand, a large family can mean more social support and more love. Therefore it can foster a more loving, cooperative child. It all depends on the TYPE of family.