So, IF they are looking for it, chances are high that it will be detected, due to the continual, regular and ongoing use. HOWEVER, mydogfifi is much better equipped to answer as to the specifics of this particular drug being on the list of what is normally tested for.
Please see link below with mydogfifi's answer - as a hair follicle drug testing specialist.
https://www.askmehelpdesk.com/addict...st-792741.html
From the reading I have done, from multiple sources, suboxone is not one of the "common" substances tested for, keep in mind, though, that the particular place of employment may have its own set of "standard" substances that it tests for. It could also make a difference if this is pre-employment testing, or after an accident, random testing, etc.
Sorry I cannot be of more help here. Most of these type of questions are posted in the "Addictions" forum, you might get more replies there, although - you will also get more personal opinions on using a controlled substance w/o a prescription.