Show outline around overlayarea

Yes, you can add this. This is a somewhat more sophisticated version in which can be switched on and off by, well, a switch.

documentclass{beamer}
makeatletter
newififbeamer@show@overlayarea
pgfkeys{/beamer/overlayarea/.cd,show frame/.is if=beamer@show@overlayarea,
show frame/.default=true}
beamer@show@overlayareafalse
mode
<presentation>
{renewenvironment{overlayarea}[3][]{%
  pgfkeys{/beamer/overlayarea/.cd,#1}%
  beamer@animht=#2relax
  beamer@animwd=#3relax
  setboxbeamer@areabox=vbox tobeamer@animwdbgroup
  strutbegin{minipage}[t]{beamer@animht}%
  % Make the minipage behave like the main part of the slide
  normalfont
  raggedright
  }
  {%
  end{minipage}endgrafvfil
  egroup
  wdbeamer@areabox=beamer@animht
  htbeamer@areabox=beamer@animwd
  dpbeamer@areabox=0pt %
  ifbeamer@show@overlayarea
   bgroupfboxsep=0ptrelax
   hspace*{-0.4pt}vspace*{-0.4pt}%
   fbox{boxbeamer@areabox}hspace*{-0.4pt}vspace*{-0.4pt}%
   egroup
  else
   boxbeamer@areabox
  fi 
}}
makeatother
begin{document}
begin{frame}[t]
frametitle{W/o show}
begin{overlayarea}{textwidth}{3cm}
      only<1>{Some text for the first slide.Possibly several lines long.}
      only<2>{Replacement on the second slide.}
end{overlayarea}
end{frame}

begin{frame}[t]
frametitle{W/ show}
begin{overlayarea}[show frame]{textwidth}{3cm}
      only<1>{Some text for the first slide.Possibly several lines long.}
      only<2>{Replacement on the second slide.}
end{overlayarea}
end{frame}
end{document}

If you want to switch the frame on for all the overlayareas (except for those for which you say show frame=false), you can use

pgfkeys{/beamer/overlayarea/show frame=true}

at some point in your document after which this change takes place.