I get majorly dizzy when I have anxiety or panic attacks. Even if I'm in a stressful situation and not really feeling anxious. I get it so bad that it feels like all the blood drains out of me and I feel like I am just going to melt into a puddle. Sometimes it makes my ears buzz when it's really bad. Alas.... I have never fainted.
I have fainted before from drinking too much back in my drinking days and once when I jumped out of bed too fast after waking up. But, I have never passed out from the dizziness that comes from anxiety.
I don't know if you have started the free 12 week CBT program offered by this site, so in case you haven't (and I strongly urge anyone who suffers this nightmare to take advantage of it), this is what is known about fainting and panic / anxiety: "People with panic attacks often experience dizziness, lightheadedness and blurred vision and feel like they're going to faint. The basic fact is that people do not faint as the result of panic attacks. Some people with panic attacks also have times when they faint, but even then they don't faint during their attack. People who are afraid of needles, blood and injury tend to faint more than other people. However, the fear response of these people (fainting) is very different from the fear respose experienced by people with panic disorder (fight or flight). The symptoms associated with fainting (reduced heart rate and blood pressure) have to do with the body 'shutting down' rather than 'gearing up' for action. You can't shut down and gear up at the same time." (Taken from an insert in the Panic Program)
When you're panicking, your body is gearing up due to the natural fight or flight response. So, even though it may feel like you're going to pass out, it won't happen when you're feeling dizzy due to anxiety / panic. The physical aspects of sudden drop in heart rate and blood pressure just isn't happening when you're anxious - in fact it's quite the opposite because your heart rate and blood pressure goes up.
Long winded as always ;p but I hope that helps.