Does dead yeast result in a stickier dough? I'm trying to troubleshoot my pizza dough. I've made it twice and both times it was too sticky to knead.

The first time I figured that I killed the yeast (the package said don't go above 140°F and I took the water off the stove when the thermometer read 140°F), so the second time I used water that was 128°F, reading the thermometer right before adding the yeast and sugar. The yeast bubbled a bit but I'm not sure if it was as frothy as it's supposed to be.

The recipe I'm using is to mix 1 package of yeast with 1¾ cups of warm water and ½ tsp sugar, then add to 4 cups pastry flour and ½ tsp salt.

I've made bread before and this dough is nothing like what I'm used to. Flouring the counter top and wetting my hands does nothing to prevent the dough from sludging. I also tried mixing it with a wooden spoon for a few minutes, hoping it would thicken. Would dead yeast cause the stickiness, or am I just preparing it wrong?
No, the dead yeast (if it was dead at all) has nothing to do with the stickiness. 

Your dough has 87.5% hydration, which is unusually high. It also uses, for some unclear reason, pastry flour, so it will behave like much higher hydration. 

The stickiness is absolutely to be expected with this recipe. If you have never done high hydration doughs, maybe you want to start in a more gradual way, maybe something like 80% with bread or at least AP flour, and and when you are OK with this go on to work with wetter recipes. Also see What can I do to keep high hydration dough from sticking to my hands? for how to become a bit more comfortable working with sticky dough. 



If you don't know how to arrive at the number: 
1.75 cups of water is 420 g 
4 cups of flour is 480 g 
420 is 87.5% of 480, so your hydration is 87.5% 

You can repeat the calculation for other bread recipes.