I don’t see any reason why you couldn’t do this if you’re used to using your phone for everything! You might have a little trouble navigating depending on your display or you might have to zoom in but nothing that isn’t an easy fix! It should be grand.
I started out using my iPhone and that’s all I’ve ever used. It’s all you need. Yes it can be a bit fiddly sometimes but it affords you a lot more freedom than a laptop or desktop does. Most sites are mobile friendly these days so crack on is what I say!