In a sense, but there are layers here. First of all, the reference to "death" here is not physical death, but a separation from God. Death in the Bible is not a judgment but a "wage" (as you have pointed out here in Rom. 6.23). Death is more alienation from God than it is the cessation of life (technically there is no cessation of life). It is earned recompense. N.T. Wright says, "Death is the denial of God's created order."
In Genesis 2, death was not a judgment but the declared and forewarned eventual outcome of their decision and behavior. They will be forbidden to have access to the Tree of Life. Death is a break of fellowship with God.
So all sins have the consequence of alienation from God, but there are degrees of punishment, as I outlined in my post, so there are degrees of "sin-ness," as Jesus himself said in John 19.11.