If you chose to install the system that monitors throttle position, then yes. It is activated the entire time. It is computer controlled (and adjustable) to spray when all selected variables are met. For example, if you set the parameters for "full throttle, 3000rpm", then you will be spraying N20 into the engine so long as those conditions are met, or untill you empty the bottle

. When you lift your foot to shift, the spray will stop until you go full throttle again.
If you flip the arming toggle off, you can go full throttle all day long (even if the bottle is still open) and never spray any nitrous into the engine. Bottle has to be on, switch has to be toggled to the "armed" position, and then some form of activation device (button or throttle sensor) must be engaged for it to work.
With computer controlled systems, many more variables are controlled than people may think. Fuel, timing, nitrous injection, A/F ratio monitoring (for shut down if unsafe conditions are detected, etc) can all be tuned to the driver's preference.
Now obviously the system described above is more expensive (but not as expensive as buying a new engine because you just blew yours for not taking precautions), so most kits you will see on the street will be dry kits with manually activated buttons ($400 is all you need for the base kit). Any of the kits can be safe, as long as you're not stupid about it.
A stock car isn't going to be able to handle a 500hp dual stage kit

. The Camaro SS loves N20, and responds very well to it, but it has limitations. My friends will not put anything larger than a 150 shot without putting in forged internals. A 4cyl, however, will only be able to handle about 50 (some say 75max, but I think that's pushing it) without beefing up the bottom end.
Damage occurs to the engine when the car is not tuned properly for N20, or a driver attempts to manually use the N20 when safe conditions are not present, or when someone simply gets greedy (more HP is simply a nozzle swap away). Nitrous is very controllable in terms of how much horsepower you want to add, and when/where you want it to be added. This is exemplified by the dual stage setups where you can control the amount of the first stage and second stage shots independently. You can adjust when each stage is engaged.
It's also important to note the surprising effects of N20 on cars that already have forced induction. Not only does N20 add HP, but it also has a cooling effect which makes turbos and superchargers more effeciant. The heat produced by forced induction robs quite a bit of horsepower, and makes consistant lap times difficult.
For example, on my friend's naturally aspirated Mustang, he has a 150 shot on it. He origionally Dyno'd at 250RWHP. With the 150 shot, he pulled 358RWHP (remember these are numbers at the wheels, not flywheel). So he gained 108 on a 150 shot. I strapped a friend's kit on my supercharged cobra just for fun, but only chose a 30hp nozzle. Before the nitrous, I made 450RWHP and 470RWTQ. After a measly 30hp shot, my numbers jumped to 480RWHP and 567RWTQ..a gain of 30hp at the WHEELS, but a huge jump of 97lbs of torque. It was the improved effeciency of the supercharger thad made the gains, not so much the N20 itself. Same holds true for my friend's Supra (turbo).
In my opinion though, the use of nitrous should be restricted to the drag strip. You will empty a bottle of N20 (usually comes in 10lb or 12lb sizes) LONG before the end of a road race. Also, bottle pressure and temperature must remain at optimum levels to receive maximum benifits, which might be hard in a long road race, I'm not sure. They make electric bottle warmers, but I'd be more concerned of it getting TOO hot, rather than not hot enough during a race.
Anyway, this got longer than I intended, but I hope it helps people who have never used N20 understand that there's much more to it than you see on TV, and that it is a viable (and sometimes elaborate) modification to add to a vehicle. As for it's use in GT4, it should duplicate real world applications, nothing more.