Not necessarily. You could also read this as the person in the comic being their preferred gender in every panel, but is just altering their gender expression towards something they’re happier with. Also, not everyone thinks about their gender that way. Some people really have thought about their gender in an aspirational way. I certainly did when I first started trying to figure out my gender.

The sentence also says “who” instead of “what,” implying that you can be the person you want to be, but not an animal, god, or tree, as those are all not people. I think it’s also fair to assume that the comic’s statement is within reason. If someone interprets this comic to think that they can become a tree, that’s a bad faith interpretation.