Can a person who has suffered trauma and is under influence of medical pain killers legally sign a medical power of attorney?

It is a very fact-specific matter. The mere administration to a patient of painkillers (or other drugs) is not a complete disqualification of what the person signed. IF an opponent of the document could show by witnesses and medical/nursing charts that the patient was not lucid at the time of signing, there is a chance of presenting the enforcement of the document.