Following up on my comment: Cirkuit converts TikZ diagrams into images by running something like the following sequence of commands:
pdflatex img.tex
pdftops -eps img.pdf
convert -density 300 img.eps img.png
Here img.tex
would be a LaTeX file that follows this template:
\documentclass{article}
\usepackage{tikz,amsmath,siunitx}
\usetikzlibrary{arrows,snakes,backgrounds,patterns,matrix,shapes,fit,calc,shadows,plotmarks}
\usepackage[graphics,tightpage,active]{preview}
\PreviewEnvironment{tikzpicture}
\PreviewEnvironment{equation}
\PreviewEnvironment{equation*}
\newlength{\imagewidth}
\newlength{\imagescale}
\pagestyle{empty}
\thispagestyle{empty}
\begin{document}
\begin{tikzpicture}
% (your TikZ code goes here)
\end{tikzpicture}
\end{document}
If you are able to use Cirkuit or a similar editor, or write a script for yourself to put your diagram into that template and run the appropriate tools, you'll have a quick way to convert TikZ code into a PNG image.
To answer your question more directly... no, I don't know of any way to convert a TikZ diagram directly to PNG without going through a PDF file (or at least DVI) at some stage.