I already know constant stress can cause a loss of interest in sex, but can it also cause a woman to not have an orgasm?

Of course. Most people forget that one way of withholding a partners pleasure in sex, is not to enjoy it. Finally, stress is a distraction, and anything so complex as an orgasm will be shelved by the brain. One paradox: many drugs used to treat stress and depression, serotonin reuptake inhibitors, severely blunt the ability to achieve and orgasm. Drugs like prozac, zoloft, celexa, or Lexapro (escitalopram) are like this.
Sure. It's all related. Wrong setting, wrong person (even if you are alone), timing, too much on the mind, lack of sleep, fatigue, meds, alcohol, drugs, anxiety, depression, bad diet, hormonal changes (innate or brought on by stress), other factors can all play a role in desire (libido), and performance (including having an orgasm).