Tikzpicture with overlay takes up space

This tikzpicture environment must be embedded in a paragraph, for example at start or end

\section{Not amazing}

\begin{tikzpicture}[...]...\end{tikzpicture}%
Text of the paragraph

If it's put between paragraphs, it will interact badly with all spacing features. Vertical space won't disappear at page breaks, baselineskip space will be inserted, \addvspace won't know about a space before that environment.

It should be TikZ's job to recognize that such an overlay environment mustn't do anything to the current page and reserve it for the shipout. Even with atbegshi there are problems:

\AtBeginShipout{\begin{tikzpicture}[...]...\end{tikzpicture}}

causes the output to be shifted down (with an overfull vbox warning) again because the TikZ picture produces an hbox.

If you can make do with at most one overlay picture per page, you can use the background package (see also TikZ overlay picture influences text around it):

\documentclass{article}
\usepackage{tikz, showframe}
\usepackage[pages=some]{background} 

\begin{document}

\backgroundsetup{opacity=1, scale=1, angle=0, contents={%
    \begin{tikzpicture}[remember picture, overlay]
    \node [circle, fill=red!90!black, minimum width=15em] at (current page.center) {};
    \end{tikzpicture}}}
\BgThispage

\section{Amazing movable type!}    
\end{document}