I don't think that assumption can be made, no. My understanding is that the purpose is generally not to be able to put more pesticide on the crop, but for the crop to react less to the amount of pesticide necessary to provide the desired environment for the plant; and this is only in the case of pesticide-resistance modifications. There are, for example, GMO rice strains which are intended to increase yield in pesticide-free crops, and in cooler climates than typically desired for rice.
Regarding herbicide: "By 2016 there was a 100-fold increase from the late 1970s in the frequency of applications and volumes of glyphosate-based herbicides (GBHs) applied, partly in response to the unprecedented global emergence and spread of glyphosate-resistant weeds.[5]:1"
But i was mistaken on pesticides, the GM for plants to create Bacillus thuringiensis bacteria leads to a reduction in the requirement of pesticide.
EDIT: but this is not about what two HN commenters believe to be right or wrong, it's about the ability for consumers to discern for themselves what is right or wrong.
I agree with your closing point, but I think there's a distinction to be drawn between labeling for pesticide/herbicide residue rates, and labeling for GMO. There's nothing about GMO that requires the use of pesticide, and some GMOs are intended to eliminate the need for pesticide application. If they change the microbiome or gross chemical composition of the plant, then that's a different matter altogether.