Can the chemicals injected for a PET scan result in low white blood count readings?
Highly unlikely. Here's why: Positron emission tomography, more commonly known as a PET scan, is a type of radiology that uses very small amounts of radioactive material, called radiotracer, to find certain kinds of abnormalities in the body. The scan then looks to see where that tracer accumulates in the body, and this information can help a physician diagnose disease. It's extremely rare to experience side effects from the radiotracer, whether it’s been injected or swallowed. The amount of radiation produced by the tracer is very small, similar to the amount of radiation a person is exposed to during a CAT scan of the chest, and the body usually eliminates the tracer within 24 hours. Plus, the substance is usually designed to have very short-lived radioactivity, so even if the tracer doesn’t leave the body quickly most of the radioactivity goes away within several hours.
So there's simply not enough radiation exposure to affect a person's blood cell count. That said, since the tracer is itself a chemical, it's possible -- though rare -- for a person to have an allergic reaction to something in the tracer. But such allergic reactions typically don't cause low blood counts.
If you or a family member has a white blood cell count that's low, a PET scan is very unlikely to be the cause, and I would encourage you to discuss your concerns with your doctor.