Norway 1940 and German naval containment

If Norway in 1940 invited the Allies in and Germany could not counter-invade, would the German submarine service be mostly confined to the Baltic?

Germany could still use the Kiel Canal to reach the North Sea, but an Allied or effectively defended Norway would make operations beyond it far more difficult for U-boats and surface ships.

The answer distinguishes absolute confinement from severe operational pressure. Norway would not necessarily need to invite an Allied occupation if its own forces fully alerted and used their fortifications effectively. Germany would still have the Kiel Canal, so submarines could reach the North Sea rather than remaining trapped in the Baltic. Allied aircraft flying through Norwegian bases could nevertheless watch the approaches, refuel, rearm, and make movement beyond the North Sea far more difficult. The immediate naval lesson is that geography and air staging can restrict operational freedom without physically sealing every exit.