Since Piloswine becomes Mamoswine after learning Ancient Power, would a Swinub become Mamosine after learning it from breeding (since they are on the same evolutionary chain)?
No, because Swinub doesn't evolve by knowing ancient power, Piloswine does. And you can't hatch Piloswine from an egg. Swinub evolves into Piloswine via level up, which you can't do as it hatches. So there is no way of hatching a Mamoswine.