No, and it is not "the same logic" at all.
Scripture is clear all have sinned and fallen short of God's glory (Isa. 53:6, Rom. 3:23) and through the one man's disobedience sin and death have come to all because all sinned (Rom. 5:12). Scripture does not place the causality on God or imputation. Adam is assigned causality, and he is assigned causality even though Eve was the first sinner! The best we could say in regards to divine causality is the structure of creation is that if a person disobeys God they then die (Gen. 2:17). What God specifically stated was "if you eat.... you will surely die," but we know from Romans five it was not that the forbidden kiwi was poisonous; it was due to the act of disobedience.
It is a design metric.
Automobile manufacturers design cars and trucks to run a certain way with certain maintenance aspects and certain prohibitions, all of which are specified by the manufacturer. For example, most cars in the US are made so they can run on 87 octane that is no more than 10% ethanol. Some cars are permitted to run with 15% ethanol. Most cars CAN run with 15% ethanol but long-term use of that much ethanol will eventually damage the motor. Alternatively, it is possible (although more financially costly) to run the auto on straight gasoline with zero ethanol, and premium gasoline usually comes with additives prolonging the life of the engine. So there are options. In this case there are several options. A person can choose, A, B, C, or D but choosing the option of poor gasoline will result in damage to the motor. The manufacturer did not
cause the damage, but the manufacturer did "
cause" the conditions by which that damage would occur of more effective, healthier options were not chosen. The cause of any such damage lays squarely with the one who does not follow the manufacturers original design specification and maintenance recommendations.
You can eat the fruit from any of the trees but one.
Hey! Let's go eat the fruit of that one tree from which God told us not to eat and see if what He told us would happen will happen.
The manufacturer did not impute the damage; it is a simple cause-and-effect relationship between design specifications and recommended compliance. The same sort of analogy can be made with the human diet. Eating healthy provides better quality and quantity of life (generally) and while it is possible to eat all the chocolate and drink all the soda one desires, that diet will have adverse effect. Likewise, arsenic and antifreeze CAN be ingested, but doing so is fatal. Manufacturer's design specifications. You're free to choose but you are not free to choose absent consequences.
Disobedience brings death, not God.
I believe this is what Paul is referring to when he mentions
"the law of sin and death" (Rom. 8:2). Simply put, if you sin then you die.