The question is begged: Is the propensity to sin, sin itself?
No. A propensity to sin is merely a desire to sin. But then you get into willful sin vs. unintentional sin. Paul discussed his desire to sin and his unintentional sins in Romans 7. He lusted for things, i.e., he coveted. To covet is to sin. He laments that his desire leads him to sin. It's that desire that is the propensity to sin. James goes into it as well:
Jas 1:14 But each one is tempted when he is drawn away by his own desires and enticed.
Jas 1:15 Then, when desire has conceived, it gives birth to sin; and sin, when it is full-grown, brings forth death.
Notice that there is a desire first. That is the propensity to sin. But only when sin "is full-grown" that it brings death, meaning the sin has to be completed. But that is for an
intentional sin. To covet is unintentional but still sin. That is mostly what the sacrifices of the old testament were meant for:
Lev 4:27 ‘If anyone of the common people sins unintentionally by doing something against any of the commandments of the LORD in anything which ought not to be done, and is guilty,
Lev 4:28 ‘or if his sin which he has committed comes to his knowledge, then he shall bring as his offering a kid of the goats, a female without blemish, for his sin which he has committed.