It happens, but it is not the standard. Most work release inmates follow the schedule of whatever employer they are working for, and many employers observe major federal holidays like Veterans Day with closures. When the employer is closed, there is no work assignment and the inmate stays at the facility.
However, some employers do operate on holidays, particularly in industries like retail, hospitality, food service, and certain government functions. Work release inmates placed with those employers may well be working on Veterans Day or other holidays, depending on their employer's schedule.
The short answer is that it varies by inmate and employer. It is not a blanket policy either way. If you are trying to figure out whether a specific person will be working on a given holiday, the best source is the work release facility itself or the inmate directly.