Not necessarily. Testosterone needs to be converted into DHT, which requires certain enzymes. Consider the basis of how Finasteride works... it does not lower testosterone levels, but, it inhibits the enzyme that converts the testosterone into DHT.
In effect, someone can have LOW testosterone, but if they have high levels of the DHT-converting enzymes then they will have high levels of DHT.
Conversely, someone can have their testosterone levels raised, but if the levels of the converting enzymes remain constant, this rise in testosterone may have no, or little effect on DHT levels in the body.
I hope I got it right... if any of you boys in the know see a flaw in my logic, or in how I tried to describe the process, please holla back.