Yes in majority of the ocassion, it matters who is the submitter. A story submitted by a strong Digg user has more chance of getting Digg votes..
It's actually not at all about who submits it. Digg makes up for power users by raising the amount of diggs they need. For example, if someone has had 300+ front page success stories, they need 200-300 diggs to make it to front page now, so they struggle just as much as everyone else. The system is quite fair. The thing is, you need to digg other people's stuff and comment on other people's submissions in order to establish a bit of a reputation, because otherwise no one will hear about you, and will think you're just another spammer (there's a lot of spammers on digg, we hate them!) Becoming a digg user that can on occasion make a lot of stuff go front-page, is extremely difficult, and requires years/months of establishing reputation and submitting high quality stuff. There was a guy on digg that exploited this system, by making friends on digg and then submitting crappy content or spam, or advertisement, and he was immediately banned. He was like top #15th digger ever, but he submitted too many low quality things...