Not necessarily. It's important to emphasize that the social superiority of Alphas comes from other people looking up to him due to the higher value they've (subconsciously) perceived of him.

People recognize an Alpha by his charisma, ambition, charge, decisiveness, backbone, stability, generosity, and kindness. When people see that everyone seems to like an Alpha (i.e. he's attractive), they'll respond by treating him as a superior: supplicating him to win his approval, seeking out his approval in order to be associated with him, asking him for advice so that they can be more like him, etc.

But an Alpha doesn't need to "come across as superior" because he already is superior and therefore doesn't give a fuck about competing with others for a high status. Why would he compete for something he already has?

For example, my boss is a young, successful and good looking dude. I willingly take the "Beta role" to him at work because it's in my best interest to seek out his approval before submitting my work, to pick his brain for knowledge about anything I don't know (I get to learn something new while making him feel smarter than me, it is a win-win situation), and to give him credit for my work rather than taking it all for myself. He's above me in the corporate hierarchy, and therefore my course of action must be to "know my place" & more importantly, to make my boss look good (which is how all promotions happen). It's simply my best strategy to acquire power in the long-run. Never outshine the master; make him look good and he'll reward you.

And to be honest, by willingly granting my boss the "Alpha" status in the workplace, the guy really likes me a lot (he's actually told me this a few times as a reason why he never shits on me when I fuck something up). So instead of trying to seem superior in our interactions, my boss focuses on offering his help so I can progress within the company and in my career, bullshitting with me about stuff that has nothing to do with work, and opening up to me about the personal shit that's going on in his life. Ultimately, this social prerogative within the workplace will be advantageous for the future of my career, since it largely hinges on my likability in the eyes of my superiors.

So it's not necessarily a good thing to always be "Alpha" since there are clearly certain situations in which being "Beta" is more strategically advantageous. That said, it is absolutely crucial for a man to know what "Alpha" is & how to gear his behaviors toward filling that role, since it's an important part of being successful not only with women, but with life in general.

This is the very reason why Olivia Fox Cabane, author of The Charisma Myth, has a clientele which is mostly comprised of CEO's and high-end corporate executives who she coaches on learning charisma. Being handed a status is one thing, but maintaining that status and using it to lead a successful life requires the underlying charismatic "Alpha" behaviors to support it.

Hope that clears some things up for you.