Of course not. The skills and infrastructure needed to run criminal organization are vastly different from those to run a business in a regular market. Apart from that, I don't see the problem with former drug lords turning into 'regular' companies, as long as they stick to the rules of the 'regular' market, which they'll have to if they want to succeed. It's not like Proctor & Gamble goes around beating people up to maintain their edge in the diaper business.
Secondly, it will of course not solve all violence. But it will at least solve the assassinations (and the collateral damage that comes with it) that directly stem from doing business in a lawless world (there is no way to enforce contracts in the underground except by violence and reputation) and it will take away much of the necessity to commit petty crime by small time criminal junkies.
Depending on which country you look at, 20 to 60+ % of prison populations across the world are incarcerated for drug-related offenses. Are you honestly going to argue that all of those people will switch to robbing banks or other violent crimes when drugs are legalized? There are basically three ways to illegally make money nowadays: drugs, violent crimes (including property crimes which may not be 'violent' in the standard definition such as night-time burglary) and fraud (white collar but also smuggling cigarettes etc.) Many of the people who are now in the drug business will simply not have the opportunity to switch into a different field even if they wanted to!
And yes I did read Freakonomics, I don't know what your point is there. While an entertaining read, a quote from a single guy who may or may not be the 'drug lord' he's claiming hardly makes for a convincing argument to defend current drug policy on. It's quite obvious that 'solving' poverty (whatever that may mean, considering that 'poverty' is such an ill-defined concept) is a good way to eliminate crime. It's not something that can be reached with policy though, at least not in the near term. Drug policy is much more contained and within reach of the legislature (by definition even), if it weren't for all the people who oppose drugs on ideological and/or mis-informed factual grounds.