A crocheter asks if they can use a sewing machine to sew on labels to Bernat Blanket yarn. I won't say yes or no, but I will give you an analogy and let you decide. But I wouldn't. Some of you may have succeeded, but it's not true for everyone.
Problem with Thread
Using thread on a crochet project when the yarn is sandwiched between the thread can be like flossing your teeth, except you go too far and cut your gums with the floss. It's sharp. It's like trying to cut clay with thread versus yarn. You will most likely have more success with the thread for this application than yarn. But it's a rotten outcome if the thread cuts your yarn project.
It's why, in crochet patterns, you usually don't use thread to attach garment pieces. The thread has the potential to cut the yarn.
Bernat Blanket has a core of fragile thread. It's easier to break with your hands than Lily Sugar'n Cream cotton yarn. Thread on a project such as Bernat Blanket has the increased risk of the thread cutting through the core of Bernat Blanket.
I suggest avoiding the sewing machine on an application like this and using similar yarn. For the Bernat Blanket, I would use cotton or even value acrylic like Bernat Super Value or Red Heart Super Saver.
We use yarn instead of thread when we add fleece to a crochet project.
Have you completed this project. Show me!