Physically, yes. Officially, no.

The governor of the state could (under most state rules) technically pick the replacement for the senate seat if the current senator is unable to perform their duties.
However, the state of Kentucky recently changed that rule to one needing a special election which kinda goes into effect august 3rd and seem to be also therefore delaying the need for one by propping up his corpse.

There is also this rather helpful write up

Great song