Oh, absolutely.
Gender presentation informs and reinforces gender identity. If I present my best appearance as my true self, it is very reassuring to my inner self. My dysphoria fades away, not merely from the initial burst of euphoria at being myself, but in a persistent effect that lasts over as many days as I can continue to present myself properly.
On the other hand, if I present as well as possible in the gender opposite my identity, I am not a happy camper, no matter how my appearance is praised by others. At the back of my mind, that little sensation of "But, you're wrong" is constantly nagging and eroding my self esteem and confidence.
So yeah, outside appearance definitely impacts how I feel on the inside. If it didn't I've have no need for all this therapy, not to mention my wardrobe and cosmetics. 😉