Absolutely - use the Jacobs chuck, intended to hold drill bits, as a stopper chuck. Pick up a 3/8x16 bolt at the hardware store, and cut the head off, and then mount that it your Jacobs chuck. Or buy a length of 3/8x16 allthread and cut off a short length.
Then, drill and tap the hole in the stopper blank, and screw it on the threaded rod in the Jacobs chuck, and then turn away. If your Jacobs chuck mounts using a morse taper, use a drawbar to keep it from backing out of the headstock. And prudent turners always use a livecenter in the tailstock to hold the blank in place for rounding - once its down to a cylinder, you can back away the livecenter to do the final shaping and sanding.
You can also make a dedicated stopper chuck from a scrap of wood. Mount it on the lathe (drill and tap it to screw onto your headstock spindle, or mount it on a faceplate), and using your Jacobs chuck to hold a bit, drill a 3/6" hole exactly on center. Unmount the block, and then run a 3/8x16 bolt through the hole with a little epoxy under the head. Remount the block, and now you have a dedicated stopper chuck.