The answer is No and it never was
Northumberland has always been Northumberland England
Though Berwick has been faught over for centurys
http://en.wikipedia.org/wiki/List_of_mo ... orthumbria
Shows it is England as early as 600bc
Hadrians wall was never built as a Scotish/ English boarder
it was bulit to mark the limits of Roman power
The Romans couldnt handle us Northumberians
It also saw very few battles it wasnt really built to keep out the Scots
But actually a trading post and tax
each side moved from one to the other but they made those on the North side pay a toll to cross the wall. Those on both side traded with each other.
The Romans wanted to have a visual barrier from those they ruled and those they didnt to try and have some sort of control over the comings and goings of the opposition
Northumberia used to be much bigger it actualy use to stretch as far south as the Humber
Sorry i am going on a bit

I will stop now
Any way to answer is no and it never was