Yes, I believe it can. Not just stress, also anxiety which is closely related, can trigger it.
Stress however might be only partially responsible, as the hair-loss problem happens downstream of the stress cascade. There is quite a lot of anecdotal evidence related to hair loss and stress. Stress, as well as some substances - for example caffeine, teine, whatevery you call it, raise the flee-or-fight body response: they stimulate a release of adrenaline (=epinephrine) which becomes a part of stress response in our organism. Unlike many other hormones adrenaline does not exert negative feedback to down-regulate its own synthesis. Abnormally elevated levels of adrenaline can occur in a variety of conditions.
Next you have cortisol, a steroid hormone, more specifically a glucocorticoid. It is released in response to stress. Cortisol counteracts insulin and inhibits the peripheral utilization of glucose (causing insulin resistance). The more resistant body to insulin, the worse it fares health-wise. There are studies that deal with high insulin resistance and hairloss -- and actually early male-pattern baldness could be a clinical marker of insulin resistance.
The worst part of stress however might be the oxidative stress which comes from free radicals destroying cells due to low levels of beneficial anti-oxidants. For example (and I AM a prime example here in this particular case), late nights spent in artificial lighting conditions may lead to disruption of nightly melatonin secretion, which is one of the most powerful antioxidants body makes. In my case it probably led to gradual deterioration of gallbladder and bile secretion, giving me gallstones (note:self-diagnosed). Guess how much sleep stressed people get... there you have it. You get stressed, no sleep, nightly light, no melatonin, greater oxidative damage to most cells, including hair follicle cells. Also when stressed you eat $h!t food so you also get less anti-oxidants from food. Do you see a link there?
To sum up: I believe body/hair doesn't react nicely to stress, regardless if it is just induced by a foreign substance several times a day. There might be a caffeine/stress threshold different for each individual because after I stopped with caffeinated coffees, I noticed my shedding has altogether stopped. While I still get a daily coke, it has most probably no negative effect on my hair.
Bottom line: When you have stress, don't get any caffeine. You deal with stress by taking it easy, sleeping it off at night and eating good rich food.