TikZ: How to draw in a 'path picture' environment outside of the 'path picture bounding box'

Is there a way to draw outside of the path picture bounding box if drawing into a path picture environment? (For theoretical interest.)

documentclass[a4paper]{article}
usepackage{tikz}
usetikzlibrary{backgrounds}

begin{document}
begin{tikzpicture}[gridded]
fill[yellow] (0,0) circle(10pt);
fill[orange] (3,4) circle(10pt);

node[draw, thick, minimum size=3cm,
path picture={
fill[red, overlay] (path picture bounding box.west) coordinate(X1) circle(2pt);
fill[red] (3,4) circle(3pt);% not shown
},
]{a};
end{tikzpicture}
end{document}