Phil's depression is as real as his marriage. It's only a word he uses as a shield, but is not mentally equipped to even understand, and depression is literally impossible on someone with so little self awareness.
This is just his resting melting face.
I would argue that Phil IS depressed, but he's not smart or self-aware enough to understand depression as a concept. It sounds very fence-sitting and non-committing, but as you say, you need some self-awareness, something Phil doesn't have.
Emotionally speaking, Phil is basically a baby. You know how when a baby burns his hand with the stove, he cries? That's because they can't rationalize what happened, nor they can put it into words, so they express themselves in whatever way he can, so they cry. Phil is basically like that. If a comment, even an objectively constructive one, gets under his skin, he won't rationalize why that upset him, he won't find logic, nor he'll try to approach it in a mature manner, he will simply lash out and be a dick, because that's the extent of his emotional intelligence. He feels an emotion and immediately has to let it out.
I mean, does someone actually believe he's happy with his life? Not even like clinically depressed, but does anyone buy those "I'm the happiest I've ever been"? He plays games he clearly hates, he has to beg literally every hour for money, he has to put up with people (not even detractors) making fun of him all the time, he has to be a fucking dickhead to developers, other creators, his own fans and quite literally everyone. How can someone even argue he's happy? Someone with so much contempt for the world has to be depressed. Even by his own definition, he's a miserable piece of shit since he's constantly shitting on everything and everyone, which according to him is the sign of an unhappy person.
This is why I think both statements are valid, "Phil is depressed" and "he uses depression as a shield", because while he is depressed, he doesn't understand depression as a concept. He doesn't see the relation between being such an asshole and being depressed, so to him, depression is just a random word he can throw for sympathy, because his concept of depression is just feeling down every once in a while, something that is normal to feel. He doesn't see depression as anger or insecurity, so he doesn't see the relationship between his constant sperging and having to repeat how happy he is all the time.