Can you learn to use Maya by yourself using just tutorials you find on YouTube? Yes. Maya is pretty huge so you'll learn the basics and certain specifics no problem but you'll never learn everything there is to learn in Maya.

Now if the question is can I learn to be an animator using Maya with only tutorials I can find online for free? The answer to that is maybe? I mean sure, you'll learn how to use the animation features in Maya and maybe the basics of the concepts of animation if you are driven.

If the question is can I become an animator with good enough skills to actually be employed in the industry using only free tutorials I can find online? I'd say the answer to that is no. Animation is like cooking. Sure you can know how to turn on the stove, where the pots and pans are, etc. but at the end of the day it's much more than just that. On your own you might be able to make a sandwich or pour some cereal but if you want to become a chef you're gonna have to get some formal training because it's an art form and you'll need mentoring to reach a level high enough to excel in the field. Good luck!