As a PRN nurse, I don't know if they will even consider spending the money on an orientation period for only a day's worth of productivity per month. But definitely put it on the table for them to decide. I applied for a PRN position a while back and the hiring mangers, during the interview, actually tried to nail me to the fulltime position. I acknowledged that I did see that position posted but opted to apply for the PRN position for personal reasons instead. Even when I offered to occasionally sign up for hours equivalent to fulltime, but could not commit to a fulltime position, they were relentless in their pursuit. I apologized by asking if I misread the offer posted. They said no and that my application was indeed desiring a PRN pool. So, I wrapped it up by thanking them for their time in the interviewing process and left tire tracks in the parking lot.
It is better to be transparent in what you can do upfront and allow them to decide if they would accept that as opposed to agreeing to something more that would be followed with frequent call-ins and absenteeism. Good luck to you.