Thinking in terms of alpha male usually creates some vision of a domineering, caveman. I don't think this is the guy you want to model for success with modern women. For one thing, you won't smell very pleasant.
If all you want to do is increase your success with women, then there is different ways to do that. Women are attracted to many different thingsl, and no man needs to emcompass every single one of those traits. In fact, some traits are contradictary. That's why you have to see the bigger picture to make all this work. You have to have some understanding of how certain things tie together. That's why "techniques" often backfire-because the person trying to apply a certain technique doesn't understand it's function.
Men have success with women both by being elusive and by overwhelming them with feelings of deep connection. The play upon the correct emotions at the correct time in a certain way and viola, success. You will only do this by accident until you understand female psychology inside and out. Additionally, you can become a victim of essentializing by trying to apply some trait to every single female on earth and sabotage yourself that way. It's both hot and cold. Without calibration, anything you try to do will fail to work consistently. At the same time, doing the same thing without ever changing will likely continue producing the same results. One must not be afraid to fine tune or change something altogether if needed.
One thing I know that will kill success with women faster than anything else is negativity. That can be anything from constantely making fun of others in a hateful manner to refusing to go out becauase all women are X at Y bar on Tuesdays. Ruling out all that negativity and asking oneself "is this a useful way of thinking" is the fastest way I know of to get on the road to success.
As far as the "alpha man" thing goes, I use that to make jokes and women find them hilarious. That's about the only time the words "alpha male" really enter my mind. I mean, would you really consider Valentino to be an "alpha man"? Yet, he could have seduced 20 beautiful women per day if he wanted to just by letting them know which hotel he could be found in. Again, ask yourself is thinking about words which are likely to bring up a domineering caveman useful in picking up women? If you can change that definition, then maybe it won't be an issue. However, I wouldn't use that terminology outside of the PU circles
You can actually make a good opener out of finding a tape called "secrets of the alpha man" in XYZguys car at work/school/outside a nightclub. Just about anything you say based on that will have the girls rolling on the floor laughing.