fancyhead[L]{
    begin{minipage}{textwidth}
        headertext \
        begin{picture}(0,0)(geometryleft,-geometrytop)
            fbox{fancyhdr}
        end{picture}
    end{minipage}
}

top - headsep - layoutvoffset.

AddEverypageHook{
    begin{picture}(0,0)(hoffset+1in,-voffset-1in)
    fbox{everypage}
    end{picture}
}

documentclass[a4paper]{article}

newlength{geometryleft}
setlength{geometryleft}{2cm}
newlength{geometryright}
setlength{geometryright}{2cm}
newlength{geometrytop}
setlength{geometrytop}{5.5cm}
newlength{geometrybottom}
setlength{geometrybottom}{1cm}
newlength{geometryheadheight}
setlength{geometryheadheight}{5.5cm}

usepackage[
    showframe,
    left=geometryleft,
    right=geometryright,
    top=geometrytop,
    bottom=geometrybottom,
    headheight=geometryheadheight
]{geometry}
usepackage{fancyhdr}
usepackage{picture}
usepackage{calc}
usepackage{color}
usepackage{everypage}

newcommand{headertext}{Text of the first header}

fancypagestyle{fancyhdr}{
    renewcommand{headrule}{%
        hbox totextwidth{%
            color{black}leadershrule height .4pthfill%
        }%
    }
    renewcommand{footrule}{%
        hbox totextwidth{%
            color{black}leadershrule height .4pthfill%
        }%
    }

    fancyhead[L]{%
        begin{minipage}{textwidth}
            headertext \
            begin{picture}(0,0)(geometryleft,-geometrytop+3cm)
                fbox{fancyhdr}
            end{picture}
        end{minipage}
    }
}

pagestyle{fancyhdr}

AddEverypageHook{
    begin{picture}(0,0)(hoffset+1in,-voffset-1in)
    fbox{everypage}
    end{picture}
}

begin{document}
    Text

    clearpage
    renewcommand{headertext}{
        A lot longer header text \
        with \
        multiple \
        lines \
        so \
        it \
        is \
        higher
    }
    Text

    clearpage
    setlength{geometryheadheight}{2cm}
    newgeometry{
        headheight=geometryheadheight,
        top=geometrytop,
        left=geometryleft,
        right=geometryright
    }
    Text

    clearpage
    setlength{geometryleft}{5cm}
    setlength{geometryright}{.5cm}
    setlength{geometrytop}{.5cm}
    newgeometry{
        headheight=geometryheadheight,
        top=geometrytop,
        left=geometryleft
        ,right=geometryright
    }
    Text
end{document}

fancyhead[L]{%
        begin{picture}(0,0)
            put(10,-200){fbox{fancyhdr}}
        end{picture}%
    headertext
}