The short answer to this is “No”. There are studies that have shown that the heart rate increases in patients with POTS relates to fluid shifts and standing up, and not primarily to anxiety. There is another study that found that POTS patients did not have a higher rate of psychiatric diagnoses than the general population. I am sure that there are some patients with psychological issues who also have POTS, just like there are patients with psychological issues that might also have heart failure, or kidney failure or asthma.
While my family might contest this claim, I believe that I am an otherwise high-functioning typical teenage girl who has POTS. I have recently found validation of this claim by interacting with other patients. This was one of the best experiences of my life as it has given me reassurance that there are, in fact, many other mentally healthy people who, like me, have a physical illness.