The short answer to your question is "yes". In Romans 5:12, Paul states, "Wherefore, as by one man [Adam] sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned:".
In Christian teaching, this later became known as the doctrine of "Original Sin". It meant that when Adam sinned, not only did it bear personal consequences, but consequences for human nature itself, which is passed on from father to children. We inherit a sin nature, which can be said to have a proclivity (inclination or tendency) toward sin. That is why Paul went on to say, "For all have sinned, and come short of the glory of God." (Ro 3:23)
The good news is that Jesus Christ came as the Second or Last Adam. Jesus came to push the reset button on humanity, so to speak. We get a do-over when we abide in Christ! Paul went on to say in verse 19, "For as by one man's disobedience many were made sinners, so by the obedience of one shall many be made righteous." When we become born again, our old nature dies in Christ, is buried with Christ in baptism, and we are resurrected in newness of life! We are no longer bound by the old sinful nature, although we are still tempted by sin (Ro 6:3-6). But under the new nature, we receive power to overcome temptation and live victoriously. Yet another reason to rejoice for all that Jesus has done for us!