You will learn to play songs if you are learning to be a musician, but you will not necessarily learn to be a musician if you are just learning to play songs.
I have had a couple of students over the years who started their learning process by watching videos of someone playing a song they liked. They would watch over and over, try a short section, watch again, and try it again. (As a musician and a teacher, I would find that a very painful process!) They came to me wanting to learn to be a musician, but being impatient with the process of learning scales and chords and how to read music (and I move these type of students as quickly as possible through that process), they eventually reverted to watching videos and learning songs by rote. I will not say that these students will NEVER become musicians, but if they do, they will be VERY limited in what they can do. Eventually, after it became clear they were not practicing what I had suggested, we discussed why they were taking lessons, and we decided together that they were actually wasting time and money on lessons.
What does an amateur or professional musician NEED to know in order to play and learn music without someone or something teaching them by rote? They need to know the building blocks of music: scales and chords. They need to understand how to read music, how rhythm shapes intersect with the lines and spaces of pitch. They need to understand how to use their hands and body to get the best and appropriate sound from their instrument. As musicians grow and diversify they need to know how a particular style is played: a dotted eight and sixteenth in the Baroque era is different from that of the Classical era from that of the Blues style. You do not get that kind of training from watching videos of someone playing songs, or from someone promising to teach you to "play songs."
Rote playing has it's place, as well as ear training and learning to play by ear, but if that is all you are learning to do, you will not learn to be a musician. I tell my students that I am like a parent. My job is to teach you the skills you need to learn music without me, and to be able to use your skills in other situations: choirs, bands, other instruments, and composing your own music. I do not want you to "play songs," I want you to flourish as a musician.
I can read this, and you can too, if you learn to be a musician!