According to my experianced tarantula keeping friend, no. The whole body should molt, so the rest of the skin didn't molt.
Keep an eye on the tarantula. A bad molt can result in death. Make sure it's water dish is full and hold off on feedings for a bit to allow what had been shed to harden.
He said he's lost T.s to bad molts.
I hope someone else experianced in keeping tarantulas will respond as well. I asked my friend when I saw you were worried without any responses yet.
Theresa Baker
No Legs and More
Florida, USA
"Stop being a wimpy monkey,; bare some teeth, steal some food and fling poo with the alphas. "