Text spirals with TikZ using greek text

As an ignorant monolingual British English speaker, my experience with dealing with non-English fonts and the babel package in LaTeX is pretty much zero, so I have no idea how practical/useful this solution is. Also, I'm not sure the characters are counted correctly. It needs to be complied with lualatex or xelatex.

\documentclass[tikz,border=5]{standalone}
\usepackage{fontspec}
% Select appropriate font
\setmainfont{TeX Gyre Pagella}

\usetikzlibrary{decorations.text}
\begin{document}  
\begin{tikzpicture}[
  decoration={
    reverse path,
    text effects along path,
    text={%
Βρυτε λεγερε συ μει. Φιμ συ αλτερα εριπυιτ σενσιβυς. 
Ατ δεσωρε αλικυαμ εαμ. Ιυς αν θιμεαμ ομιθταντυρ, 
ετ μολεστιε σορρυμπιθ εαμ, σινθ αδμοδυμ φιερενθ αδ πρι.
Φελ συ πυτανθ φιθυπεραθα, αεκυε ερρεμ ευμ συ. Νο ευισμοδ 
μενθιτυμ πραεσενθ νες, πρω ελιγενδι σοτιδιεκυε σωνσλυδαθυρκυε ιν. 
Ιδ μεα δισιθ φολυπθατιβυς. Ηομερω ρεπρεχενδυντ μελ νε, 
αθκυι μελιυς προδεσεθ αν μει. Πρι ει δωσενδι νεγλεγενθυρ, 
κυαεστιο ρεπριμικυε ατ φελ.
}, %text in greek 
    text effects/.cd,
      text along path,
      character count=\i, character total=\n,
      characters={scale=1-\i/\n}
    }
]
\path [decorate]  (0,0)
   \foreach \i [evaluate={\r=(\i/2000)^2;}] in {0,5,...,2880}{ -- (\i:\r)}; 
\end{tikzpicture}
\end{document}

(As I was posting this, I see there's a Lua-/XeTeX solution, which I would prefer. However, here's a pdfTeX method.)

Remember each letter (in this type of TikZ picture) is typeset in its own \hbox, which allows for many effects, but comes at a cost. The Greek characters are also a problem, which I can't explain.

But you can use the older method of transliteration. Just make sure you wrap up the multi-character glyphs just as you would with other accents (e.g., {\"u}ber). Note that this \hbox method seems to make sigma be considered as a final-sigma, which you can 'fix' by grouping it:

\documentclass[tikz,border=5]{standalone}

\usepackage{ucs}
\usepackage[utf8x]{inputenc}
% Also works with these
%\usepackage[T1]{fontenc}
%\usepackage[utf8]{inputenc}
\usepackage[english, greek]{babel}

\newcommand{\en}{\selectlanguage{english}}
\newcommand{\gr}{\selectlanguage{greek}}

\usetikzlibrary{decorations.text}


\begin{document}
 \selectlanguage{greek}

\begin{tikzpicture}[
  decoration={
    reverse path,
    text effects along path,
%    text={Κε{ί}μενο στα ελληνικ{ά}.}, %text in greek
    text={Ke{'i}meno {sta} ellhnik{'a}.},
    text effects/.cd,
      text along path,
      character count=\i, character total=\n,
      characters={scale=1-\i/\n}
    }
]
\draw [decorate] (0,0)
    \foreach \i [evaluate={\r=(\i/2000)^2;}] in {0,5,...,2880}{ -- (\i:\r)};
\end{tikzpicture}

% Something a little more elaborate...
\begin{tikzpicture}[
  decoration={%
    reverse path, %
    text effects along path, %
%    text={Κε{ί}μενο στα ελληνικ{ά}.}, %text in greek
    text={{<H}dona{`i} ka{`i} l{~u}pai f{'o}boi te ka{`i} j{'a}rrh
      {>e}pijum{'i}ai te ka{`i} {>a}postpofa{`i} ka{`i} t{`o}
      {>a}lge{~i}n t{'i}nos {>`a}n {e>~ien}?  {>`H} g{`a}r yuq{~h}s,
      {>`h} qrwm{'e}nhs fuq{~h}s {s'w}mati, {>`h} tr{'i}tou tin{`o}s
      {>ex} {>a}mfo{~i}n.
 % Diq~ws d`e ka`i to~uto; >`h g`ar t`o m~igma, >`h >`allo <'eteron
 % >ek to~u m'igmatos.  <Omo'iws d`e ka`i t`a >ek to'utwn t~wn
 % pajhm'atwn gin'omena ka`i pratt'omena ka`i doxaz'omena.
}, %
    text effects/.cd, %
      text along path, %
      character count=\i, character total=\n, %
      characters={scale=1-\i/\n} %
    }
]
\draw [decorate] (0,0) \foreach \i [evaluate={\r=(\i/2000)^2;}] in
{0,5,...,2880}{ -- (\i:\r)};
\end{tikzpicture}

\end{document}