No, not bound nor compelled, but instead, changed, changed by God.
This is a description from God's point of view regarding the heart of and hence the will of natural man, the will that you say is not compelled by God to be in union with Him but instead does so by its own free will. However, we are informed in the below that the heart of the unsaved, natural man is filled with evil and with madness leading it.
How then is there truly free will, and how can it choose God?
[Ecc 9:3 KJV]
3 This [is] an evil among all [things] that are done under the sun, that [there is] one event unto all: yea, also the heart of the sons of men is full of evil, and madness [is] in their heart while they live, and after that [they go] to the dead.
[Jer 17:9 KJV]
9 The heart [is] deceitful above all [things], and desperately wicked: who can know it?
[Jhn 3:19 KJV] 19 And this is the condemnation, that light is come into the world, and men loved darkness rather than light, because their deeds were evil.
When someone becomes born again by/from salvation, and as a part of it, their will is changed by God.
[Eze 36:26 KJV]
26 A new heart also will I give you, and a new spirit will I put within you: and I will take away the stony heart out of your flesh, and I will give you an heart of flesh.
[Heb 10:16 KJV]
16 This [is] the covenant that I will make with them after those days, saith the Lord, I will put my laws into their hearts, and in their minds will I write them;
[2Ti 1:7 KJV]
7 For God hath not given us the spirit of fear; but of power, and of love, and of a sound mind.