Is a youthful offender under the green case able to use any probation time as part of his time served

Generally no. Probation and incarceration are two legally distinct forms of supervision, and time spent on probation does not count as time served toward a custodial sentence.

The distinction is fundamental. Time served refers specifically to time physically incarcerated, whether in a jail, prison, or in some cases a residential treatment facility that functions as a custodial placement. Probation is a community-based supervision program that allows a person to remain free, albeit under conditions and oversight. Because the person is not incarcerated during probation, that time does not reduce a sentence the way jail or prison time does.

For youthful offenders, the rules around sentencing, credit, and what counts toward time served vary by state and by the specific program or disposition involved. Some states have youthful offender programs that allow for more flexibility in how time is credited, and the specific case you are referencing, the Green case, may have particular provisions attached to it that affect how the sentence is calculated. That is a question that requires a specific answer from the attorney handling the case, since the answer depends entirely on the terms of the disposition and the applicable state law.

What can sometimes be argued is that time spent in a secure residential program as a condition of probation may qualify as a form of custody, depending on how restrictive the placement is and how the state defines custodial time. An attorney familiar with youthful offender sentencing in that jurisdiction is the right person to evaluate whether that argument applies here.