How can I check if a header has an ending full stop?

Firstly it is always best to post a MWE. As you have not posted one I am posting a general answer, for exact formatting of the section you will need to add your own formatting commands.

You don't need a \futurelet. TeX keeps track of special codes for letters and punctuation to place the right amount of space after a stop. We can check the value of the \spacefactor macro and add a stop or do nothing if it is already there.

\newcommand\@addpunctuation[1]{\ifnum\spacefactor>1000\else#1\fi}

The rest of the code are minor details. Here is the MWE.

\documentclass{article}
\makeatletter
\newcommand\@addpunctuation[1]{\ifnum\spacefactor>1000\else#1\fi}
\newcommand\buildhead[1]{#1\@addpunctuation.}
\DeclareRobustCommand{\addhead}[1]{\buildhead{#1}}
\DeclareRobustCommand\Section[1]{\addhead{#1}}
\def\section{\secdef \starcmd \unstarcmd}
\def\starcmd[#1]#2{\bfseries\Large\addhead{#2}}
\newcommand\unstarcmd[1]{\bfseries\setcounter{section}{O}\renewcommand\thesection{\Alph{section} \addhead{#1}}}
\makeatother
\parindent0pt
\begin{document}
\makeatletter

\section[small title]{Testing}\\
\section{Testing}\\ % remains as is 
\Section{Testing}\\
\Section{Testing.}
\end{document}

If you want the macro to work both for \frenchspacing and \nonfrenchspacing, you can try:

\newcommand\@addpunctuation[1]{%
   \nonfrenchspacing
   \ifnum\sfcode`.=1000
     \ifnum\spacefactor>1000\else#1\fi
   \else
      \ifnum\spacefactor>1000\else#1\fi
      \nonfrenchspacing
  \fi
}

and test with

\frenchspacing

Test. \fbox{A test test}

\nonfrenchspacing

Test. \fbox{A test test}

You can also visit the link quoted by Philippe Goutet in the comments below.

The problem can be solved at a macro level without 'meddling' with the space factor.

\documentclass{article}
\makeatletter
\usepackage{catoptions}
\robust@def*\newsection#1{%
  \begingroup
  \edef\currtitle{\cpttrimspaces{#1}}%
  \def\currlabel{}\def\lasttok{}%
  \xifinsetFT{\detokenize{\label}}{\cptoxdetok\currtitle}{}{%
    \def\reserved@a##1\label##2##3\cpt@nil{%
      \def\currtitle{##1##3}%
      \def\currlabel{\noexpand\label{##2}}%
    }%
    \expandafter\reserved@a\currtitle\cpt@nil
  }%
  \def\getlasttok##1{%
    \expandafter\ifx\@car##1\@nil\cpt@nnil
    \else
      \edef\lasttok{\unexpanded{##1}}%
      \expandafter\getlasttok
    \fi
  }%
  \expandafter\getlasttok\currtitle\cpt@nnil
  \s@expandarg\ifinsetTF\lasttok{\dots\ldots\textellipsis}{%
    \@tempswatrue
  }{%
    \begingroup
    \lccode`\X=133
    \lowercase{\endgroup\expandafter\expandafter\expandafter
      \ifstrcmpTF\expandafter\@car\lasttok\@nil X}{%
      \@tempswatrue
    }{%
      \@tempswafalse\let\elt\relax
      \def\siso@do##1{%
        \xifinsetFT{\detokenize{##1}\elt}{\cptoxdetok\currtitle\elt}{}{%
          \@tempswatrue\loopbreak
        }%
      }%
      \siso@@loop{.!?:\dots\ldots\textellipsis}%
    }%
  }%
  \def\elt{\expandcsonce\currtitle}%
  \cptexpandarg{\endgroup\section}{\if@tempswa\elt\else\elt.\fi\currlabel}%
}
\makeatother

\begin{document}
\newsection{Test section.\label{sec:1}}
As seen later in Section~\ref{sec:this} \ldots.
\newsection{Test section}
\newsection{Test section.}
\newsection{Is this a test section?}
\newsection{Heh, this is test section!}
\newsection{Test section\dots}
\newsection{Test section\ldots}
\newsection{Test section\textellipsis}
\newsection{Test section\label{sec:this}\ldots}
As seen earlier in Section~\ref{sec:1} \ldots.

% I have accounted for the ASCII character 133 but you may not get it to print:
\newsection{Test section …}
\end{document}