I suppose it also depends on the yeast species. Not for all the yeast species certain conditions are stressful. Let's take some of the non-Saccharomyces species - there are some methylotrophic species which certainly "do not mind" being in the environment full of monocarbonic xenobiotics (e.g. methanol, formaldehyde). These species get their carbon from such compounds, so obviously - it won't be stressful for these cells. But te presence of same contaminants will surely be lethal to some other species. Therefore the mentioned yeast cells certainly produce different enzymes.
Were you to test non-conventional / non-Saccharomyces yeast species gaining carbon isolated from unusual or contaminated places (e.g. monocarbonic contaminants), I would suggest measuring the AOX production.