Yes, they will void the warranty on the specific system that I modify, and any system that the modifications directly effect. So Mazda could deny me warranty for prematurely worn bushings due to the stiffer springs/shocks, but they couldn't deny me warranty if the radio craps out, for example. But I'm OK with that.
I didn't buy the vehicle new to get the warranty. I bought it because I wanted the newer styling, the larger displacement of the 2.5 (knowing I would turbo it), and the 6-speed. I looked at used 2012 mz5's, but I got a brand new 2013 with 3 miles for about $1500 more than most were asking for used 2012's with 30k miles.
I enjoy and feel comfortable doing maintenance and repairs myself, and don't really mind shelling out the hundred bucks and spending a half hour in the garage to change a swaybar link. In fact I prefer that over either waiting in the dealer waiting room drinking stale coffee leafing through old magazines, or dealing with carpooling to drop-off/pick up the car.
In the event something truly catastrophic happens, well these aren't really expensive engines/transmissions. I would definitely be more hesitant if I was dealing with a brand new BMW or Porsche, where sourcing a new engine could easily be over $10k (I have historically been a german-car guy). That said, I'm not looking to make 400+whp on my stock engine - I'm thinking 250-ish, which should keep things reliable, and is probably near the practical useable maximum for a front driver (especially with no LSD).