When you're sitting in front of a grand jury wondering how you're going to pay $75,000 in legal bills and explaining why you had to shoot somebody75 feet away in self defense, the trigger pull will be the least of your worries.
Seriously, though, I think a LOT of people buy self defense guns and don't think about trigger pulls; I've pointed out the different between double action only (DAO), double/single, single, etc. to several people and they stared at me like I was explaining particle physics: utterly clueless.
In the crushing, paralyzing, suffocating stress of a face to face self defense situation, you won't be aware of your trigger pull, but a long double action pull can still throw your accuracy way off, for obvious reasons. It won't be that much of a factor at point blank range, but anywhere past 4 or 5 yards some DAO guns will require a ton of practice and feel to hit a target.
This is why I personally prefer a double/single gun like my SIG 2022. The long DA first shot acts as a safety, then subsequent shots are nice, crisp, SA pulls. Or, if I have a half second, I can just thumb the hammer back and the first shot's SA as well.