Sure it does; can God give a gift that is counterfeit? God gave me free will; so free it is.
How can a "gift" be something that can and does stand a good chance of sending you to hell?
Some "gift."
No, men believe they are free because they can decide what time to wake up in the morning and what shoes to wear with what pants. And while all that feels very personal and individual and immediate, the course of every atom was determined by God from before the foundation of the world.
That frustrateth the tokens of the liars, and maketh diviners mad; that turneth wise men backward, and maketh their knowledge foolish; That confirmeth the word of his servant, and performeth the counsel of his messengers" -- Isaiah 44:24-26"Thus saith the LORD, thy redeemer, and he that formed thee from the womb, I am the LORD that maketh all things; that stretcheth forth the heavens alone; that spreadeth abroad the earth by myself;
This is joyous news for grateful believers who owe their faith to the Holy Spirit opening their hearts and minds and illuminating God's truth. But it's news of no consequence to those who don't believe since they are already lost in the darkness of their denial.