The standard breakpoints used in clinical susceptibility testing (Kirby-Bauer/disc diffusion assay) are considered reliable when every part of the testing method is standardized. If you change any part of that standardized method without properly validating those changes, it may or may not affect the outcomes and there would be no way of knowing without some sort of comparison study for validation.
Difficulty obtaining the proper media would seem common enough that this exact problem has been studied. This study did a head-to-head comparison of nutrient agar (NA) and Mueller-Hinton agar (MHA) for susceptibility testing on 149 clinical isolates along with a few QC reference strains. They found that NA agar did not produce acceptable results for the QC strains according to the relevant Clinical & Laboratory Standards Institute (CLSI) guidelines. Use of NA also resulted in many errant determinations among their clinical isolates (including many isolates of Staphylococcus aureus).
Given the error rates in this study, I would say that you should not rely on susceptibility testing results using nutrient agar in any sort of clinical context.
Nassar, M.S.M., Hazzah, W.A. & Bakr, W.M.K. Evaluation of antibiotic susceptibility test results: how guilty a laboratory could be?. J. Egypt. Public. Health. Assoc. 94, 4 (2019). https://doi.org/10.1186/s42506-018-0006-1