No, no, no. This is all wrong. He isn't asking for his coat, he has lots of coats. What he's looking for is BLOOD. He says so after he puts the coat on and turns the collar up. He wants blood because blood means excitement and possibly a murder mystery to solve. Sherlock enjoys solving the crime as Donovan points out in "A Study in Pink". So no, he's not in love with his coat, and these love theories about Sherlock are getting rather out of hand.