Exactly. OP, by all means learn the tools available today; you'll never be commissioned to paint a website in gouache. Just beware: it's easy to get locked in to using Illustrator and only ever coming up with things you can make in Illustrator, for example. That makes for a shitty designer.

Nothing wrong with gouache though, in fact you can learn a lot about color just messing around with some paint for a while. A lot more than you'll learn from pixels.

My advice in a nutshell: play with a lot of different mediums and look at a lot of different work if you really care about being a designer.