Dual Avelyn build
Solution 1:
No, the Avelyn is found in a metal chest and Bonfire Ascetics don't reset those. The only way to get a second Avelyn from this chest is in NG+ or you could have another player drop one for you online.
Another way to get more Avelyns is in the Doors of Pharros area (Brightstone Cove Tserolda in SotFS), by killing the red phantom Bowman Guthry, who only appears if you play offline and can repeatedly be killed by using Bonfire Ascetics.