No. Currently, only registered scouters can edit advancement for scouts, with the exception of the scout themselves or their parent/guardian who can mark things Completed but not Leader Approved or Awarded.
However, a scout could mark it Completed, and add a note indicating who signed it off. They could even, if they have the technology to hand, attach a photo of the handbook page with the date and initials.
ETA: There are several help articles on using Scoutbook available at https://help.scoutbook.scouting.org. I linked to several of the “getting started” ones in a prior post on these boards.
