\version "2.12.3"

#(define (thin-line grob) 
  (let* (
    (pos (ly:grob-property grob 'positions))
    (lo-hi (interval-widen pos -1.2))
    (thin 0.05))
  (make-line-stencil thin 0 (interval-start lo-hi) 0 (interval-end lo-hi))
  ))
%

\new StaffGroup \with { 
  connectArpeggios = ##t 
  \override Arpeggio #'X-offset = #0.6
  \override Arpeggio #'stencil = #thin-line
} 
<<
  \new Staff { c' c'\arpeggio  c'' c''\arpeggio }
  \new Staff { b  b \arpeggio  b'  b' \arpeggio }
>>