Yes they are, or at any rate the foreigners in them are.
Just as much as the Swiss, Irish and German regiments of the 18th century French army, or Frederick the Greats’ Freikorps “blue on blue and damned to hell”.
No, they are not mercenaries, they are there to serve the nation’s government, they are not free lancers working for whoever pays them.
For instance, in France it is illegal to be a mercenary, but not illegal to volunteer to serve in a foreign army.
I have an application from the Legion that I decided I would not use because of the five year minimum, and I have received offers to do mercenary work, and have sought mercenary work, I never saw them as the same thing.