What you lose by not trying is the use of the motherboard.
You lose nothing additional by attempting to solder the capacitor in place; because solder flowing in, along the capacitor lead, might reestablish those via connections for you, again.
Drip liquid flux along the capacitor leads, so that it runs into the PC board hole. Use a 45 Watt soldering iron, heating the capacitor lead, and running the solder onto the lead, right at the point where it emerges from the PC board. Over-solder the connection as much as you can without shorting adjacent pads or PC board traces.
If the repair is successful, you will have gained a functional motherboard. If the repair is not successful, you will still have the non-functional motherboard that you have now.
In the future, don't drill-out component leads from PC boards, unless you are positive that you are dealing with--at most--a double-layer PC board.