Fuller's two DS9 episodes were Empok Nor (meh IMO) and The Darkness and the Light (ugh IMO), and he had story credit for both. Neither were arc-related stories, though Empok Nor became a location for a future story. His work on Trek didn't heavily involve any ongoing story arc, but that's not to say he isn't talented in this (especially given Hannibal). Many of this VOY teleplays leveraged past continuity a fair amount (Raven, Relativity, Workforce), so he seems to have talent in putting in nerdy references in stuff, which we fans love.
I'm only worried about the notion that he may want to give his show the "60s fun". This can be interpreted in many ways, but I'm recalling a claim made of EVERY series after TNG that the newest series would bring back the "TOS feel", with "more action". Each show arguably tried in different ways: DS9 tried some frontier themes before becoming a war epic, VOY had a greater emphasis on exploration and far less reliance on accountability than TNG, and ENT continued that trend with IMO a better result.
Who knows what Fuller will bring to the table. He certainly has the pedigree NOW that he didn't have when he started out on Trek, and I'm sure it will show - as such I'll be cautiously optimistic as we slowly hear about the concept, casting, and staffing on the show. Will he bring in talent from the previous era to work on the look of the show? Will he staff his writer's room with fans, or new blood to promote a different take?
In the end, I think the little details like the continuity or ship specs will matter very little unless they have good people making the stories up, and good people making the stories look good on screen, and we know you can't force that. Fuller seems to really be a step in the right direction and it's the right kind of early news to break to the public. I trust we'll have more, and soon.
Mark