It is straightforward to synchronize the coordinate systems of eso-pic with an overlay tikzpicture.
\documentclass{beamer}
\usepackage[texcoord,grid,gridunit=mm,gridcolor=black!30,subgridcolor=gray!10]{eso-pic}
\usepackage{tikz}
\begin{document}
\begin{frame}[t]
\frametitle{A slide}
\begin{tikzpicture}[overlay,remember picture,x=1mm,y=-1mm,shift={(current
page.north west)}]
\draw[-latex] (40,40) -- (60,60);
\end{tikzpicture}
\end{frame}
\end{document}

And if you are willing to append remember picture to every TikZ picture you can literally use your suggested notation.
\documentclass{beamer}
\usepackage[texcoord,grid,gridunit=mm,gridcolor=black!30,subgridcolor=gray!10]{eso-pic}
\usepackage{tikz}
\tikzset{textpos/.style={overlay,x=1mm,y=-1mm,shift={(current page.north
west)}},every picture/.append style={remember picture}}
\begin{document}
\begin{frame}[t]
\frametitle{A slide}
\begin{tikzpicture}
\draw[textpos,-latex] (40,40) -- (60,60);
\draw [textpos,color=yellow,fill=yellow!25] (0,0) -- (10,0) rectangle (20,10) -- (30,10);
\end{tikzpicture}
\end{frame}
\end{document}
eso-picto draw a grid? beamer has a build in grid option:\setbeamertemplate{background}[grid]– samcarter_is_at_topanswers.xyz Jan 15 '19 at 09:56textposkey? – samcarter_is_at_topanswers.xyz Jan 15 '19 at 09:59\begin{tikzpicture}[overlay,remember picture]then you can merge in arbitrary additionaltikzpictures later. (I am not saying that theeso-picgrid won't work, however using TikZ for all of these makes things simpler.) – Jan 15 '19 at 15:42