Technically, a poolish might be viewed as transitional between the sourdough process and a straight dough process using commercial yeast. Its benefit and value comes from the compounds, like alcohol and acids and esters, that are produced during the period of prefermentation and ultimately contribute to the flavor and aroma and texture of the finished crust. There are essentially three effects of the poolish on the dough into which it is incorporated. The first is that the acids produced during prefermentation strengthen the dough by tightening up the protein such that the gluten has higher elasticity. This effect suggests that one needs to be careful with the amount of poolish to use because too much acid can create an overly elastic dough. Second, the addition of the poolish to the dough lowers the pH. This has the effect of increasing the shelf life of the crust (or bread) by delaying the staling process and inhibiting mold growth. Obviously, this is rarely a concern with pizza, which is most often consumed rather quickly. Finally, the organic acids and other compounds contribute to the flavor and aroma and texture of the finished crust. The poolish is perhaps the favored approach for artisan bakers who make baguettes.
The downside to poolish, or any other preferment for that matter, is that it takes time to prepare and manage them. Out of necessity, commercial bakers have no choice. For home bakers, preferments may be inconvenient because they have to fit within one's work and/or home schedule and, hence, requires careful planning. However, I think they are a useful tool on one's arsenal of pizza making tools.
In terms of a NY style pizza dough, it is fairly straightforward to convert the dough formulation for that style, and others as well, to a poolish format. Of course, some experimentation may be required, but if one follows the more or less standard approach to preparing and managing a poolish, good results should follow.