I don’t think August was related to Henry’s adoption. Surely not.
But the adoption took place, and it means that it was part of the initial plot to break the curse. It is twisted enough as to come from Rumplestiltskin’s mind.
I agree, no one but Emma could break the curse. But… in any situation? under a particular circunstance? Maybe. And it is also possible that even being enough an Emma’s kiss to her husband -Neal- or her son -Henry- in a hypothetical “happy ending of Neal/Emma relationship”, the drama of adoption, 10 years of solitude, blablabla, was neccesary to fulfil other gaps in the plot: for instance, kill the dragon and recover the true love potion that brings the magic back.