\version "2.11.41"
\score {
  \context Staff <<
    \context Voice << 
      \dynamicUp
      \relative c' {
        % Clearly, here the "cresc." needs to be high above the staff
        \setTextCresc 
        c4\<_"Default" c' e' c,\!
        % When hiding the line, the "cresc." should not calculate its position
        % including the invisible line
        \setTextCresc \override DynamicTextSpanner #'dash-period = #-1.0
        c,4\<_"Hidden, way too high" c' e' c,\!
        % Trying to set the style to something like none does not work (solid line!)
        \setTextCresc \set crescendoSpanner = #'none
        c,4\<_"style=#'none" c' e' c,\!
        
        % This produces the output that I want, but unfortunately it's not a 
        % dynamics mark and the extension of the spanner is lost (just in case 
        % Lilypond some day is able to export e.g. to MusicXML that's relevant 
        % information!!!)
        c,4^\markup{\italic "cresc."}_"normal text markup" c' e' c,
                
      }
    >>
  >>
}