No, Escoffier would not say otherwise.
To start the Bearnaise sauce, you first make a redux of tarragon, shallots peppercorns, vinegar........Hollandaise you do not.
Bearnaise does not have lemon juice as a prime ingredient!
I guess if you want to be a shoemaker, you could add a redux at the end of a batch of Hollandaise. I've seen that done before but I cringe at the sight of it. That's a hack move!
Any other questions?