Possibly, and it is worth understanding what programs actually move the needle on a release date versus which ones do not.
In the federal system, the most significant program for early release is RDAP, the Residential Drug Abuse Program. Successful completion can result in up to twelve months off the sentence plus earlier transfer to a halfway house. That is a real and meaningful reduction, but eligibility requires a documented substance abuse history that predates incarceration. If that history exists and he has not already enrolled, his case manager needs to know about it immediately given how close the out date is.
The First Step Act also created earned time credits for completing approved recidivism reduction programs and productive activities. Federal inmates can earn ten to fifteen days of credit for every thirty days of successful program participation, and those credits can be applied toward earlier transfer to home confinement or a halfway house. With a November out date, time is short but not necessarily too short to earn some meaningful credits if he is actively enrolled now.
In state systems the programs and credits vary significantly by state. Some states have educational completion credits, vocational training credits, or specific treatment program credits that can reduce time served. The specific programs available at his new facility and what credits they carry is something his case manager can answer directly.
The honest reality is that with an out date in November the window for program completion is narrow. The more useful benefit of enrolling now may be the halfway house placement that comes with certain program completions, which gets him home earlier even if the official out date does not change.
Have him talk to his case manager at the new facility as soon as possible about what is available and what the timeline looks like.