We had a discussion about a long time ago. Answer is no. There's a reason there are seven CAPITAL sins, the sins to which all other sins reduce.
WRATH/ANGER are a different category than LUST. If WRATH/ANGER reduced to LUST, then it wouldn't be a capital sin, but would just be an effect of lust.
Is it possible that being prone to one category can make one more prone to the other, but it's not necessarily the case.
Even some of the saints who were very pure had issues with anger/wrath. In fact, the more one has impurity under control, the greater the tendency sometimes to be tempted to wrath or anger.
Also, there are TWO different effects of Original Sin ... concupiscence (lust, desire) and irascibility (anger, wrath, rage).
In fact, the men I've known who are more given to sins of impurity tend to be more passive and less aggressive than those who have them under control.