I don't think so as Celtic with few exceptions have always struggled in Europe in recent times.
I think the clues were Martin O'Neil who took Celtic to a Euro final but came up short at Villa and Sunderland. Neil Lennon who famously mananged Celtic to a victory over Barca, but despite starting well at Bolton, ultimatley failed. Walter Smith at Everton, and there could be other examples as well.
Then there's the players. Kenny Dalgliesh was a legend at Celtic and had the same impact at Liverpool, then also won the EPL as a manager. But that was a while ago. Since then the only player in my opinion who could and should have made a major impact on the EPL was Tierney, but injuries made that impossible.
Andy Robertson deserves a good mention as well.
However there is plenty of evidence that managers and players who have been greats in Scotland have failed to reach anything like that level in England, and that's what the Spurs board missed.