Is disobeying the Word of God the same thing as denying the Deity of Christ,
since the Word of God is Christ?
Odd question, or, rather, odd comparison.
Disobeying the Commandments of God or Christ is a sin if that is what you are asking. Will disobedience of Him not separate us from Him? This part of your question (in my opinion) is directed more to believers, as unbelievers live in disobedience of Him willingly whereas believers should be striving to live Christ-like, or, in obedience.
Denying the Deity of Christ is directed more at those who do not profess to be a Christian. One can hardly profess to be a believer in and disciple of Christ if one denies Christ and His Deity can they? Why would they? Scripture says to worship the Creator, not the created. To deny the Deity of Christ is to lower Him to being just another creation of God, and not the Second Person of the Godhead/Holy Trinity. If one believes Jesus was created, and just a flesh and blood man like every other man God created, why on earth would they profess to be His disciple, or put any faith in Him? After all, they have asserted He is just a flesh and blood man...........as are we all, and hardly worthy of worship or praise.
So, generally speaking, the answer to your question would be "No." Even believers, who acknowledge the Deity of Christ, can be disobedient to His Commandments.........knowingly or not.
He is surely the "Living Word," as the Holy Bible is the "Written Word." And believers/unbelievers can both disobey, fail to follow His Commandments/live in disagreement with Scripture. However, only unbelievers deny the Deity of Christ. Believers, those who are believers in and disciples of Christ proclaim His Deity.