Some research for you
"Prostitution follows addiction in 48% of the subjects, precedes it in 38%, and is simultaneous in 14%"
(James, 1977)
"They found that the average age at first heroin injection and first prostitution was similar (19.0 years for heroin vs. 19.2 years for prostitution) and that 44% had used heroin prior to prostitution entry, 26% subsequent to entry, and 30% at about the same time as entry."
(Gossop, Powis, Griffiths, & Strang, 1994)
"To assess the sequence, timing, and prevalence of sexual and illegal drug use milestones in prostitute women, we interviewed 237 prostitutes in the community and 407 comparison women at an STD clinic. Drug use was more commonly reported by prostitutes than comparisons [...] Sexual- and drug-related milestones occurred in the same order in both groups, with drug use preceding sexual activity and injecting drug use preceding prostitution. Ninety-four percent of prostitutes who injected drugs reported noninjectable drug use before prostitution, and 75% of prostitutes who injected drugs reported doing so before beginning prostitution. [...] Currently, there is little theory to guide our understanding of why such events occur in the order they do. The available data suggest considerable variation in the forces, both internal and external, that affect women's lives and move them toward drug use, drug injection, and prostitution (in some order). At least one pulp fiction version would have us believe that women are lured into prostitution by drugs and that the latter serves to maintain the former, but the available literature suggests that the true situation is more complex and heterogeneous."
(Potterat, John J., Rothenberg, Richard B., Muth, Stephen Q., Darrow, William W., Phillips-Plummer, Lynanne, Journal of Sex Research, 00224499, Nov98, Vol. 35, Issue 4)
The general consensus seems to be that drug use and prostitution are related, and the relationship varies depending on the individual. Drug use is particularly problematic among street prostitutes, where drug users become prostitutes to pay for their addiction, and their addiction contributes to an overall stressful work environment (which is in turn relieved by more drugs).
Escorts sometimes begin drug use after beginning regular sex work, but the link seems to be more facillitative than causal (that is, people want to do drugs, but cannot until they get a job which allows them to afford it. This is similar to any job which comes with a substantial increase in money, such as a business executive) Drug use in general is far rarer among escorts than other prostitutes, and drug use is discouraged in the world of "high class" prostitutes in general: