Yes. Yes he does.
It’s a bit of a sensitive topic, Sirius’ hair. It hasn’t been short since second year, and Mrs. Potter is the only one allowed to trim it a little in the summers, so by sixth year it’s well past his shoulders. It’s nice and shiny too, soft looking but not greasy, the perfect sort of hair to run your hands through. If you were allowed to, because Sirius will actually hex you if you touch his hair without permission. That, or dramatically fall to the floor.
"My hair! My only weakness! I am dead, goodbye forever!"
"For the last time, Sirius, you’re not Samson." James says as he drags his friend away.
But whenever Remus is sitting down, unguarded and relaxed, Sirius will suddenly appear, wurm himself around until his head is in Remus’ lap and demand, “braid me”
Remus sighs but puts down his book anyway, hands starting to smooth out the tangled knots in Sirius’ hair. “You’re a spoiled puppy, you know that?”
"I’m a delightful ball of joy, now scratch behind my ears while you’re at it."