Link is most definitely a person. While he's meant to be a connection to the player, he clearly has his own life, his own story, and his own ambitions. Yes, I agree that Link is a "link", but I personally think that the link is to make the player feel like they're involved in the story, which is basically part of Link's life.
If Link had no emotion, there would be no motivation to get anything done. For example, in Majora's Mask, when Skull Kid transforms Link into a Deku Scrub, it's obvious that he was horrified. His face alone was enough to make we want to strangle Skull Kid right there. If Link just looked like, "Meh. Whatevs." I probably wouldn't have cared much, if at all. In the Wind Waker, when Aryll was kidnapped, Link didn't plan on saving Aryll when he got around to it. She was his sister and he loved her. As she was carried away, Link almost ran off a cliff chasing after her. He wanted to save her now. In Twilight Princess, after Link and his friends had been attacked by the bokoblins, you could see the terror in his eyes. He was scared for his colleagues. It's clear that Link has emotion, therefore, he is his own character; he is a person.
As for what the developers intended, I would have to say I think they were going for both. I think that Link's emotions and ambitions were meant to connect with the player. The player controls Link and experiences what he does. Because the player is "in Link's shoes", it almost makes us feel how he would. In my experience, when Midna made her snotty remarks to Link, it made me mad at her. It felt like she was insulting me. When Miaku died on the ocean, I felt like it was my responsibility to carry out his last wishes. I think the developers wanted Link to be a person, but I think they also wanted to link the player to his experiences. Like they wanted us to feel how he would if he were a real person.