Transfer puree to sieve set over bowl and strain, pressing with rubber spatula to extract as much pulp and juice as possible. Sweeten sauce to taste.
Do ahead: Blackberry sauce can be made 1 day ahead. Cover and chill.
Place nectarines in medium bowl. Sweeten to taste, tossing with sugar 1 tablespoon at a time.
Let stand 15 minutes. Spoon some sauce into bottom of 6 sundae dishes. Top with 2 tablespoons nectarines, some pecans, 2 scoops ice cream, more blackberry sauce, and more nectarines.