I had my exam for NROTC a month ago and the closest thing I did to a drug test was piss in a cup so I don't think they do. Not exactly sure though because I didn't mark anything on the medical history survey admitting to drug abuse.
All I can tell you is DS' DoDMERB was urine only; no blood or hair samples. I was pretty astonished that they don't draw blood for a standard health screening; forget about drug tests. They even draw blood for my annual civilian workplace health insurance / wellness screen; triglycerides, cholesterol, etc etc. Just seems like health test 101 for me but what would I know.
DODMERB is basically just a medical history exam to make sure you meet required criteria. Thru the urine sample they can come up with several things that could indicate drug use, not pin pointing the drug in your system. (sample would be called a non-negative) in which case you might have to provide further samples.
DS had random drug test at his ROTC unit quite frequently. Not sure if all schools do it. He went to MEPS since he did SMP and it was a much more intense physical exam.