Disclaimer: I don't know how useful this will be for your particular use case.
However, it is possible to add a single point to a shape in Inkscape at an object's midpoint/rotation centre. You could then potentially group both shape and that point, and use that point as the animation centre.
Here's an example, and how I would achieve it in Inkscape.
Draw a regular polygon or any shape, and switch on Snapping, and Snap Centres of objects. The center of a polygon will be the object centre in Inkscape, if you have a normal path, you can click a shape twice to enable the rotation handles and drag the rotation centre to anywhere you desire.
Draw a short straight line from that center
- Open up the XML editor, delete the last two numbers of the path, then press enter to confirm. Perhaps rename the path ID to "center" so you easily reference it.
Now you have a point - an invisible path with only one node, called "center"
Open up the Objects panel, select both paths and group.
Here's the SVG if you want to try playing with it
<?xml version="1.0" encoding="UTF-8"?>
<svg width="210mm" height="297mm" version="1.1" viewBox="0 0 210 297" xmlns="http://www.w3.org/2000/svg">
<g transform="translate(59.3 -5.86)" fill="none" stroke="#000" stroke-width=".5">
<path d="m-22.6 45.8c-1.89.97-9.84-8.64-11.6-9.79-1.79-1.16-13.8-4.45-13.7-6.58s12.4-4.2 14.3-5.17c1.89-.97 10.8-9.73 12.5-8.58 1.79 1.16-2.56 12.8-2.67 15-.107 2.13 3.05 14.2 1.16 15.2z"/>
<path id="center" d="m90.4 42.4"/>