Just to give a slightly different gloss to that, PV, because there are some myths about the Scottish origins of the American episcopate, the first American bishop, Dr Seabury, asked to be consecrated by Church of England bishops, but they declined because they were not empowered to consecrate anyone unable to take the oath of allegiance. He was therefore consecrated by Scottish bishops.
Indeed. The CoE was, after all, a state church, and prayers for the reigning monarch were a part of the fundamental liturgy.
Of course, that was not a barrier to being in communion with them or even outright unity, as Anglicans and Lutherans attempted such a feat soon after we formally kicked the Pope out. The fact that it sadly failed doesn't, of course, nix the idea that it is impossible.
Soon after, Parliament passed an Act allowing CofE bishops to consecrate non-citizens serving abroad without the oath, and so the second, third and fourth American bishops were consecrated by Church of England bishops: White and Provoost by the Archbishops of Canterbury and York and the Bishop of Bath and Wells; and Madison by the Archbishop of Canterbury and the Bishops of London and Rochester.
Actually, the fourth was the same as the first: ++William White. ++Samuel Seabury was second, and ++Samuel Provoost was third.
Those three bishops White, Provoost and Madison with their Church of England lines, dominate the American lines of succession.
Actually, until later, they were the only ones. ++Samuel Seabury consecrated two bishops, but they in turn did not consecrate any further ones. Still, the Scottish legacy lives on today not only in the American BCP, but in the fact that
many official liturgies throughout the Anglican Communion have at least elements from it.
However, my point was that our first line was Scottish, which did mingle for a brief period of time with the English. Furthermore, it was
because of the Scottish succession that the English line was made even possible: the people there were worried about a new Jacobite ally.