I think the key to dealing with emergencies is the weekly review. Emergencies happen everywhere, probably every week if not every day depending on your responsibilities.
Just responding to emergencies may be keeping with GTD or it may not. It depends on how well and completely your managing and tracking your actions/projects. If you're not managing and tracking you're probably allowing for more emergencies.
Just for some perspective. I've been working the GTD system for a little over 18 months and just in the last 3 have I really begun to nail the weekly review. I actually started using GTD in the midst of a multiple big time emergencies, because I had to do something.
Connect is a really great resource. One of the earlier podcasts on the weekly review has been really helpful as well as the weekly review checklist (I use it every week). So be patient here's my general progression with GTD, for what little perspective it may offer you:
1. redid my office to be suitable to GTD
2. week 3 - cleared backlog (It took 3 weeks upfront, but it was worth it)
3. month 4-5 got and kept IN's to empty
4. month 12 - nailed capture and processing (omnifocus on my iphone, omnifocus on my mac - omnifocus, omnifocus, omnifocus - just sayin')
5. month 15 - redid, upgraded my office to better suit my implementation of GTD
6. month 16-17 established a consistent effective weekly review
7. what's next for me? Seeing if there's improvement to be gained on working more in context mode.
Your never done learning GTD or anything else. Still works for me as long as my learning doesn't get in the way of my doing.