Yes, it seems from the picture that the hole in the end of the connecting rod, (red), has broken through, so there might still be the rivet in the end of the chain, (green). Making a new hole in the rod would be possible but you'd still have to remove the old rivet in the chain before fitting a new one. If the effective length of the rod ends up being shorter, the instrument will need re-calibrating.
Hold the two ends in line, and solder together.
The solder lump will never move down as far as the little pulley so will be fine.
Then use a barometer app on your phone to re-calibrate by adjusting the screw at the back.
And, yes, I've done this.