Can someone with sleep apnea take a benzodiazepine such as xanax (alprazolam)?

Sure but is it safe?: You can take anything you like but if you mean can you do it safely, that's a whole different thing. Benzos suppress breathing. If sleep apnea is severe and if you are unused to using benzos, then your risk is potentially significant. Most cases are not serious but that doesn't mean your case is mild.

Sleep apnea: More respiratory depression depending on severity of apnea and dose of xanax (alprazolam).

Advise against it: In general narcotics, benzos or any sedating medications will worsen sleep apnea as it suppresses breathing. Unless you're in a controlled and monitored setting like the hospital, I would not recommend it.