* Prometheus Unbound introduces us to the character of Lindsay Novak
Who only had something like two minor appearances on Atlantis, hardly anyone of real significance. Why didn't you include the episode Enemy Mine? It introduces Major Lorne, someone who is of importance to Atlantis.
* Avalon introduces us to Col. Landry, explaining who he is when he shows up in The Intruder
Maybe things aren't spelled out exactly in The Intruder, but General Landry's other Atlantis appearances make it clear he's the SGC's current CO. Besides, even in The Intruder his role isn't significant enough to warrant watching a two-part SG-1 episode as preparation.
But they're relevant to SG-1's story arcs, and have no impact on Atlantis and its story arcs at all. Hell, even The Pegasus Project has more relevance to SG-1 than it does for Atlantis.
* Unending and Ark of Truth are 'backstory' setup for Carter's arrival on Atlantis
No they don't. All the backstory and set up for Carter's arrival at Atlantis is covered in the first few season 4 episodes which do not draw on Ark of Truth at all. Hell, Ark of Truth was released after season 4 of Atlantis ended, so no one watching season 4 when it first aired had seen Ark of Truth at all.
* Continuum shows us what happens to Carter after she leaves Atlantis
Bu most of it is set in an alternate timeline which gets reset at the end. The only thing we see Carter do in the "prime" timeline in that movie is discuss a moon base with O'Neill. Hardly vital to getting the complete Atlantis experience.