I don't think the difficulty in testing that hypothesis is whether your samples have some chemicals in them or not. It's finding a sample population, and the collection of their samples.
That is, it's somewhere in the neighborhood of profoundly rude to approach someone in the midst of terrible grief, all, "I see you're weeping over your loss. Let me have some of your tears for science!"
You could "pre-enroll" people — say, the families of terminally ill patients — to collect their own tears when they do suffer that loss, and weep for it. Even then, though, compliance is going to be difficult to manage. Their priority in that moment isn't your experiment; it's their own devastation. And absolutely rightly so.
Having to stop, or even momentarily diminish, their weeping to fetch the sample kit — do they even have it with them? do they remember where it is? — then open it up (because it has to be sterile, right?) and jab it in their face might also have a materially deleterious effect on the grief-processing role that their weeping in that moment is supposed to provide. If so, that might also taint the results of the experiment, no?
So, no, it's not just a matter of testing for the presence of some chemicals.
(Edited for clarity and phrasing.)