In my experience the answer is "it depends".
The company I work at has a similar 'interruptive' culture. The main reason this happens is that people don't plan and therefore become disorganised, with the result that they frequently need to run around interrupting others to get their urgent requests done.
I use email to make my requests to others and to delegate but have learned that for some individuals, I just have to go interrupt them myself. For example one person does not manage her inbox at all - she has in excess of 2,000 unread emails at any one time so my email won't be seen in a timely manner. I have to go see her or I'd be waiting months. She is senior to me so I can't change her ways, I just have to manage the situation myself.
BTW I also work in a technology company. My theory is that this is still a young industry (comparatively) and therefore it lacks some of the established processes you see in other industries. Many small technology companies have been started by talented entrepreneurs and designers who aren't necessarily good managers or at least good at setting up processes.