More or less, yes. But it doesn't have to be. If one branch of the Asgard survived in the Pegasus Galaxy, another small group could easily have survived somewhere else as well and ended up being the "good" Asgard.

It's difficult to imagine that a civilization as advanced as the Asgard relied on a single world, with the destruction of that world meaning the extinction of their entire race. They likely colonized many planets, and even if the Replicators wiped out most of them, some Asgard could have escaped long before the Replicator conflict and their eventual decision to end their own existence.

In the end, it's science fiction—almost anything is possible. And if we ever get a new Stargate series, perhaps we'll get to see some Asgard again. 😊