What you say is correct, and that is one of the reasons why sugar is optional in the basic Lehmann NY style dough formulation as he devised it. If I recall correctly, member pizzanapoletana (Marco) indicated that under normal circumstances it would take an enormous amount of yeast (around 5% or so by weight of flour) to be able to exhaust the simple sugars in a dough, which I take as a confirmation of the point you made.
Tom Lehmann goes to great lengths to get pizza operators to eschew the use of sugar (as well as eggs and milk products) in the dough when the dough is to be baked in a deck or hearth-style oven. However, apart from flavor/sweetness preferences, I can recall four instances where he will accept sugar in the dough: 1) When the pizza is put on a pizza screen before going onto the stone surface (with the option to "deck" the pizza directly on the stone at the end of the bake to get better bottom crust browning); 2) When the dough (cold fermented) is to be held over for more that 2-3 days before using; 3) When the pizza is to be baked on a screen alone with a proper oven configuration; and 4) When the pizza is to be baked in a conventional home oven. It is reason 4 that always interested me and, as best I can determine, Tom allows for the use of sugar in that application because he thinks that standard home ovens don't generate sufficient BTUs to pose a problem. Unless a dough recipe I am trying out calls for sugar and the fermentation time is fairly long, I don't personally use sugar if the dough is to be baked directly on a stone or tiles. I think Tom underestimates the temperatures that many of our members are able to get or create in their home ovens.
Thanks for helping us better understand some of the fine points of dough making. I always look forward to your learned posts, my friend.