Making includegraphics placement conditional on width of graphic

You can directly use \makebox:

\documentclass[
   paper=8.5in:11in,
   BCOR=0.5in,
   twoside=true
]{scrbook}
\areaset[0.5in]{5in}{8in}
\addtolength{\voffset}{0.5in}
\setlength{\marginparwidth}{0.5in}
\setlength{\marginparsep}{1in}
\usepackage[showframe,pass]{geometry}

\usepackage{scrhack}
\usepackage{float}
\usepackage{graphicx}
\usepackage[figurename=Example]{caption}
\usepackage{subcaption}
\usepackage{newfloat}

\usepackage{adjustbox}

\newsavebox{\igbox}
\newcommand{\igdecide}{%
  \ifdim\wd\igbox<\textwidth
    c%
  \else
    \ifoddpage
      l%
    \else
      r%
    \fi
  \fi
}
\newcommand{\fincludegraphics}[2][]{%
  \par
  \sbox\igbox{\includegraphics[#1]{#2}}%
  \checkoddpage
  \makebox[\textwidth][\igdecide]{\usebox{\igbox}}%
}

\begin{document}

\mainmatter

\begin{figure}[!ht]

\fincludegraphics[width=1.1\textwidth]{example-image-16x10}
\captionbelow{Captions always centered on textwidth}

\fincludegraphics[width=0.7\textwidth]{example-image-16x10}
\captionbelow{Captions always centered on textwidth}

\end{figure}

\newpage

\begin{figure}[!ht]

\fincludegraphics[width=1.1\textwidth]{example-image-16x10}
\captionbelow{Captions always centered on textwidth}

\fincludegraphics[width=0.7\textwidth]{example-image-16x10}
\captionbelow{Captions always centered on textwidth}
\end{figure}

\end{document}