No.
It is you that need to read carefully--and apply some biblical theology.
Romans 5:15 says "But the free gift is not like the trespass. For if many died through one man's trespass, much more have the grace of God and the free gift by the grace of that one man Jesus Christ abounded for many. " "Emphasis mine)
Paul says many died through one man's trespass...and the wages of sin is? Death. Technically, could those without the law sin? No. Therefore, in some way, we were all "in Adam" when he sinned and we all, in some way, incur his guilt and his sentence. Sin and death are inseparable. After all, the wages of sin is death.
ADDED:
18 Therefore, as one trespass led to condemnation for all men, so one act of righteousness leads to justification and life for all men. 19 For as by the one man's disobedience the many were made sinners, so by the one man's obedience the many will be made righteous. 20 Now the law came in to increase the trespass, but where sin increased, grace abounded all the more, 21 so that, as sin reigned in death, grace also might reign through righteousness leading to eternal life through Jesus Christ our Lord.
Adam's sin led to condemnation for all men, not "death." Adam's sin made us sinners. Since Paul is using the chiastic structure, if you deny the simple things that he is saying, you must deny the other leg of the argument. Therefore, if we were not made sinners by Adam's sin, we cannot be made righteous by Christ. If we were not condemned by Adam's sin, we cannot be justified by Christ's act of righteousness.
Your argument will not stand.
The Archangel