I think there's no doubt that the offense is fine without Edelman, as we showed this past year. In fact it seems the offense can usually adapt to any change, so long as they have sufficient time to adjust (effectively losing Gronk right before Super Bowl 46 hurt for example).
But I think part of what makes this offense so good year in and year out (aside from Brady of course) is that they don't rest on their laurels. They took an offense that scored 31 unanswered points in the Super Bowl and traded a first rounder for Cooks. It's not so much that they NEED Edelman, but getting him back helps to keep pushing the offense forward, because you know at least one player on offense is going to get hurt or regress (it happens every year to someone usually).
Julian's return is insurance against that inevitability, and allows us to hopefully relegate more offseason assets to the defense.