Question is not completely clear to me. Do you use the SVG as button to be clicked? That would mean you are on version 11.5.  You could use the InBuilt Visited state in that case for that SVG button.

If you have another setup, you’ll need to use a shared or advanced action triggered by an event which is linked to the visit of that link. You can still use a multistate object, but the ‘Visited’ state which has the checkmark will now be a custom state, and use the Change state (or Go to Next state if you have only two states) to switch to the checkmark state.