It seems obviously so, at least to me. Ditto Lucifer and 1/3rd of the angels who sinned. Two major points come to mind.
First, God created man in his own image. God is no puppet. Thus, neither are we. Like God, man does have a free will and that free will clearly includes the power to resist God and rebel against Him.
Second, God obviously desires a father's rightful honor, a loving relationship and the Godly worship of his children. There could be little love or honor for God to enjoy from an eternal relationship with automated puppets.
I think its important, particularly when discussing sin, to note the difference between the Free Will of God, and the "Free Will" of Man.
We are made in God's like-ness, we are not God, therefore our "will" is "like" God's, but not Divine. God's will is bound to his holiness, his asaeity, his creative ability, and ultimately his unboundedness - his freedom is absolute. There is no law over him, there are no obligations to him - he is all, and all is ultimately from him. He is autonomous - a law unto himself.
Man was created bound, by simply being a creature - bound by space, by time, by the laws of the created universe - we are not autonomous. Our rebellion is likewise limited - we cannot exist apart from the universe God created, or the God who created it. Further, before Adam's initial rebellion, our will was as free as a human's can be, but after the fall, our will is no longer even that free, as scripture says on top of the chains of time and space, are the added chains of sin and death. We are called slaves to sin and death - slaves who cannot will apart from their Master's desire. Christ can set our will free from sin and death so that we can respond in faith to the Gospel, but we cannot throw those chains off by ourselves, nor will we ever throw off the chains of time and space until we are in the glorified state in Heaven. The redeemed have a freer will than the lost, but even that freedom is limited.
So yes indeed, God gave us and the angels (to a lesser degree) an aspect of Himself in that we have a will (which is really the flipside of desire), but our will is so much a small thing in comparison to God's will that in truth much of what we claim in stubborn rebellion against God we only have because he gave it to us in the first place. I think sometimes we're like children who won't eat our vegetables because we want the chocolate cake, forgetting that the same Mom that tells us to eat our vegetables is the same Mom that made the cake - we wouldn't have either without Mom. Our freedom is limited to only those things Mom put on the table.