I highly doubt this scenario, since the majority of drug sales are small transactions.
Small transactions which add up to big transactions when the mailers/dealers/manufacturers end up with lots of BTC and few ways to spend it other than to either drop it on the market or buy lots of anonymous web hosting, coffee, alpaca socks and VPNs. The thing is, BTC's nature is likely to attract black market activity far faster than legitimate business so the need for them to cash out into fiat currency is inevitable.
aside from that.... Lets say that some major distributors come online, and there is a sizeable wholesale trade (I see this as a bit more likely). The vast majority of cash *IS* used in drug transactions, right now. It may not be the majority of the markets that its used in, but, the actual dollars themselves, nearly all of them, move through drug transactions at some point.
Every few years the news media rehashes the figure of what percentage of US money tests positive for just cocaine....and its really most of it (I forget the percentage they toss around).
If there were some website where agencies could trace every dollar serial number, where it's been, and what other dollars it has touched, then that would make the analogy more accurate. There's a big difference between a hunch that "this could have been drug money" based on a whiff, versus tangible public evidence that can positively establish that the guy who just dropped 45kBTC at XYZ exchanger is a drug dealer, "let's go take him down".