Yes, he is anatomically correct.
The Tin Man was a wood-chopper who had rusted in the forest near his cabin when Dorothy and the Scarecrow met him. He sang the song "If I only had a Heart" and agreed to accompany her to the Emerald City to see if the great Oz would give him a heart. He saw the Wizard together with the party. Later, when Dorothy and Toto had been abducted by the Wicked Witch's Winged Monkeys, the Tin Man, Lion, and Scarecrow dressed up as Winkie soldiers and infiltrated the castle in an attempt to rescue Dorothy. As they were escaping with her, the witch was killed being splashed with a bucket of water by Dorothy.
Nick Chopper started out as a rather healthy and handsome human being. He was an Ozian born and raised in the eastern quadrant known as the Munchkin Country in Oz. Being a Munchkin, he was destined to become a great lumberjack woodsman. This was because when Nick was growing up his father was a skilled woodsman who chopped down trees for a living. Nick's father would sell the wood and lumber to the people in Oz to make houses, bridges, fences, and other establishments throughout the farming communities. So when Nick grew up he carried on the family tradition and became a woodsman as well. He made his own home deep in the Munchkin woods not too far off from Oz's Yellow Brick Road. He lived all alone on the side of the road in a little cottage with a bed of dried leaves.
After his parents died, Nick had no other family to turn to, so to stop his aching heart from the loneliness he was enduring after their deaths, he decided to find a mate to marry and to start a family of his own with. Soon Nick fell deeply in love with a beautiful Munchkin girl he had met by fate named Nimmie Amee. She was lovely and kind but worked as a full time maid and belonged to an old widowed woman who lived close by in the woods. But Nimmie Amee also had deep feelings for Nick, so Nick proposed to her confessing his true love. Nick Chopper then promised his significant other and future wife that he would build a nice sturdy house for her to escape to and live a happier life at, all he had to do was chop some trees down and start building. Now, This old woman who owned Nimmie Amee eavesdropped on the two lovers talking one day about their plans. Being old and alone, she did not want to lose her servant, so she secretly visited the Wicked Witch of the East. This Witch was the Wicked ruler of the Munchkin Country and had the people who inhabited the east tightly in her bondage. The old woman paid the Witch two sheep and a cow to prevent her servant from becoming a bride to elope with Nick Chopper in anyway possible. The Wicked Witch cast a dark spell and without him knowing it, she magically enchanted his axe to slip in his hands when he used it to swing. Instead of hitting the wood of the tree trunk, his axe strangely missed the spot he aimed at and over time chopped and hacked all of his body parts clean off one by one. After each accident, a nearby tinsmith named Ku-Klip who also lived in the Munchkin Country replaced the lost part that had been amputated with a new shiny tin one until eventually his entire body was made of tin, even his head. And his soul from his meat body, transferred to the tin one. But with his new form the Tin Woodman no longer had the desire to eat or drink, or even sleep. And his new tin body had no heart, so naturally he thought he could no longer love, and ultimately lost interest of pursuing a future with Nimmie Amee.
To Nimmie Amee's horror, Nick never asked her to marry him like he promised he would because he no longer cared for marriage or love. Heartbroken, Nimmie Amee disappeared and she and Nick never saw each other again.
Some time later he was caught out in the forest during a rain storm while chopping down trees to pass the time and the water quickly rusted him solid. He stood there frozen in one position for an entire year. While stuck in that same spot and terribly rusted, the Tin Woodman had a lot of time to reflect on his past. Soon he realized he still loved Nimmie Amee all this time. Even though he did not need food or rest he still wanted to love. And he wanted to find her, to love her again, thus concluding that maybe having a heart was something that he needed to have after all.
. . .