Questionable. From the POV of England Scotland was a lot less tempting than northern France.
The English succumbed to temptation, and wasted blood and treasure on the Hundred Years War (and even longer in the Gironde) fighting a war they could never win.
The highlands in particular were full of mountians and people who tried to kill you.
The Lowlands, on the other hand, are just like England, and who actually gives a toss about the sparsely-populated barbarian wasteland beyond? Lowland Scots have had more in common with the English than they've ever had with the Highlanders. Scottish Kingship has always been based on the productive Lowlands and the excellent North Sea ports (Edinburgh in particular), and regarded the Highlanders as a problem.
While some of the more ambitious english kings had a go at the place the general aproach appears to have been to rely on the northumbrians to keep the scots out on a day to day basis and more southern forces when they invaded in significant numbers.
This is because English power was being wasted on quixotic exercises in France. Victory after glorious victory, and never an end to the war. Even if an English King (Henry V, say) had become King of France the English would have rebelled against the combined kingdom within a generation or two because its centre of gravity would have been in Paris, not London (let alone York or Cardiff).
The full potential of Lowland Scotland wasn't something that the Wardens of the Marches wanted any English king to appreciate. The Percy family in the East (Earls of Northumberland, "Kings of the North"), the Nevilles in the West, and the bandit families of the Border country (Kennedys, Nixons, Armstrongs ...) they were intimately connected with in between. It was very much in their interests for the king's eyes to be turned in a completely different direction.
It took a Scot on the English throne to tell the Marcher Lords to "get tae f@&!, y'English ponce" and to put the Border Reivers in their place (which meant enlistment or transportion to the American Colonies).
Where the English
did project power advantageously to the Continent was in the Netherlands, and it wasn't as conquerors. It was based on shared interests.