Strangely enough: using an object tag when embedding the svg by reference (instead of the img tag), allows the externally referenced stylesheet to work as expected.
Code:
<object type="image/svg+xml" data="../Images/Image04_svg_links_style_sheet.svg"></object>
I suspect something deep within Chrome is the culprit.
And once the doctype is removed from the external svg file, it even passes EPUB3 validation (after being converted to an EPUB3, of course).
Still no idea how widespread the support for such a strategy would be.
Though it raises the question of whether or not Sigil should be parsing files (including those with svg extensions) for "xml-stylesheet" PIs to adjust when updating hrefs.