I don't work in the field but I have read enough to understand - yes and no. At least if I understood your question correctly, I think you're in the right ball park but not necessarily the right direction.
Conduct Disorder is essentially the medical/modern name for what used to be referred to as delinquency - a consistent pattern of antisocial behaviour, combined with a lack of empathy or remorse about said behaviour. As others have said, children/teens with Conduct Disorder don't respond to punishment but may respond to reward, and this can be used to modify behaviour.
Conduct disorder is not usually a diagnosis given until adolescence. Before this, similar behaviour patterns are identified as Oppositional Defiance Disorder (ODD). This is defined as a persistent and almost automatic rejection of any kind of authority. Essentially the medical name for a "You're not the boss of me!" kind of attitude. Note with ODD, there is nothing mentioned about empathy.
ODD is extremely common, especially among neurodivergent children, and not all children with ODD go on to develop CD.
Likewise CD can be a phase that some adolescents go through and grow out of. Some adolescents with CD will go on to be identified as being psychopaths as adults, but not all. So it is not exactly true to say that CD = Psychopathy. CD if it continues into adulthood does merge into Antisocial Personality Disorder or ASPD, but not all individuals with ASPD are psychopaths (Wikipedia says around a third are).
ODD is known to be able to be caused when parental discipline is too harsh/reactive or a combination of too inconsistent/lax but then also too reactive (think a parent who ignores or gives into their child until they annoy them, and then wallops the child, rather than intervening calmly earlier, or a parent who flies into rages unpredictably). But it can also happen without this. It can be indicative of a stress response, for example when a ND child's needs are not recognised or met, or as an indicator of possible abuse or trauma. It has a lot of overlap with the autistic PDA profile and this can be mistaken for ODD. There are also a lot of aspects of ADHD around emotional regulation and impulse control which overlap with ODD, so children can meet criteria for ODD if they have difficulty controlling their temper.
There is less research into the causes of CD but there is the fairly classic path of a child who hasn't had a great start in life/school for whatever reason that might be - ACEs or other difficult life experiences, ND, lack of opportunity to develop appropriate behaviour etc and because of a punitive/critical response to this behaviour by adults the child/teenager becomes jaded and acclimatised to punishment so that it ceases to have any effect. And then this in itself might lead to either an entrenched belief that the world is out to get me and the only way to survive is to hit back, or if the young person isn't engaging in education then they are highly likely to fall back on crime, exploitation, addiction, homelessness etc.
But yes if somebody was inherently a sadistic psychopath specifically, then it would likely show up as the path ODD > CD > ASPD > psychopathy, if this is clinically noted.
But, as said, not all psychopaths are sadistic or gain pleasure from other people's pain. Some of them just lack empathy and weight their own gain as much higher than anything relating to others. The definition of psychopathy is a combination of grandiose narcissism + lack of empathy/remorse + lack of taking personal responsibility or long term planning. A lot of psychopaths are said to be very charming and if this is the case from childhood then it might be nothing is raised.