tikz picture in eso-pic

You are overwriting the line color. I would probably just store these things in styles. Apart from solving the issue you will be more flexible, i.e. could add e.g. dashed and so on.

\documentclass{article}
\usepackage{tikz,eso-pic,xparse}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\drawlinecenter}{%
  \AddToShipoutPictureBG{%
    \AtTextCenter{%
      \begin{tikzpicture}
        \draw[center,line width=6pt]
          (0,0) -- (0,1);
      \end{tikzpicture}
    }}}
%    
\newcommand{\drawlineupperleft}{%
  \AddToShipoutPictureBG{%
    \AtTextUpperLeft{%
      \begin{tikzpicture}
        \draw[upperleft,line width=6pt]
          (0,0) -- (0,1);
      \end{tikzpicture}
    }}}
%      
% main macro:
\NewDocumentCommand{\drawline}{O{}m}{% #1-optional style arg. #2-position
  \tikzset{#2/.style={#1}}
  \csname drawline#2\endcsname
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\drawline[color=blue]{center}
\drawline[color=red]{upperleft}
firstpage\clearpage second page\clearpage third page
\end{document}