Did Rebekah decide for herself whether to go with Abraham's servant?
Yes. Rebekah personally made the final decision whether to leave her family and return with Abraham's servant. Although the servant did everything he could to woo and win her, the account says the choice came down to her, and her family called her to inquire directly at her mouth.
Les explains that even though Abraham's servant did all he could to woo and win this beautiful girl, she still had to make the final decision. After the feasting and getting acquainted in Rebekah's family home, it boiled down to her making the choice. Her family said they would call the damsel and inquire at her mouth, showing that Rebekah herself was asked and decided.
And they said, We will call the damsel, and enquire at her mouth.
And they called Rebekah, and said unto her, Wilt thou go with this man? And she said, I will go.