Cut off the remainder, drill a hole, stick a longer bolt thru, and be done... you want to go the extra mile then weld the head to the back side of the mount. (that would be the RIGHT way to go about this repair.)
You're idea wont work as well as you're thinking for a couple of main reasons.
First is the threads. If you're broken off right at the shoulder, then you'll have little to no compression on the mounting eye when it comes to secure it to the mount.
Also there's this little thing called shear force. Sure the majority of the shock will be sitting on whats left of your stud, but there will be a lot of physics at work trying to force that shock off the mount. That shock, and your safety, is relying on how good that weld is. And speaking of that.... ANY amount of difference between surfaces or burrs/slag left over from that seam, WILL have an effect on the longevity of that eye bushing. Just think "cheese grater."
CAN you get away with a repair of this nature? .... probably.
SHOULD you TRY and get away with this? ..... I would not recommend it.
Just for the sake of your parts and safety more than anything.