Jared, I am still learning my way with my own Nepenthes. There are different types so I am not sure if your plant will behave like my plant. Mine is a smaller one called Nepenthes densiflora x (spathulata x spectabile)..that is the mile long name of my little plant as written on its tag.
One thing has improved my Nepenthes, by accident, thanks to my hubby. Usually I just keep the media moist, it is growing in sphagnum moss media. Now last December while I was away, my hubby made my plant sit in water. On my return I saw that, ready to get mad, but the next day, I observed there is a considerable improvement on the pitchers, and it is actually making better leaves. So I guess in my dry location, to compensate for it, my plant will not mind sitting in water. I do not give fertilizers to any of my carnivores. But just using the rain water I was able to save last Nov. When I run out later on, I will be back to the distilled water. I also notice the pronounced red color and bigger size of one of the pitchers, which is a real marked improvement. I grow my Nepenthes indoors by our west facing kitchen window and temps indoors is at 68 to 70F, humidity inside my house is at 49%.
Before I would specifically spray the pitchers to help in the humidity aspect, but now I do not seem to need to do it, but will observe later on when summer temps return. Maybe it is coping well too with the cooler temps.
You were asking if the plant will die if there are no pitchers, it won't as long as the main plant is still alive of course. But it will need to produce new leaves to form new pitchers.
Here is a photo of mine:
The rosy colored pitcher, color more prominent and pitcher is bigger too:
A new leaf is forming, coming out of the other one it seems.
The other pitchers, smaller but holding and slowly growing:
I noticed you mentioned you have Sarracenias..I also have them, I keep them outdoors always, and sitting in water. Right now it is enjoying rain water with our on and off rains. Once rainy season is over back to distilled water again. They are dormant right now and they do need this cold dormancy.