Yes, the passenger seat belt warning chime and the passenger present systems are linked.
I can't speak about Opel directly, I'm familiar with Mazda and Honda. The way the passenger present systems works, is by using a weight sensor in the seat. The weight sensor senses below 20 kilos and above 40 kilos. If something is on the seat that is below 20 kilos the assumption is that the seat is not occupied and something may be laying on the seat like a suit case. The air bag is normally shut down at this time but the indicator may not light showing that it is off. The indicator behavior may vary.
Between 20 - 40 kilo is the danger zone. This may indicate that a car seat with a child is in the seat. This will cause the indicator to show that the air bag is off every time.
Above 40 kilos the assumption is that the seat is occupied. This will enable the air bag and enable the seat belt warning chime.
These systems require calibration. Mazda had a procedure that put the air bag computer in a learn mode and then place calibrated sand bags on the seat when prompted. Body shops brought cars in all the time for this calibration after replacing the air bag computer.
Something is clearly wrong with the system. The root cause is unclear. It may be that the connector for the seat belt buckle was left unplugged. (Most new systems will detect this but not all) On all my older cars i have this sensor unplugged causing the chime to be inoperative. On Mazdas unplugging the buckle sensor cause the air bag light to illuminate. In this scenario the air bag will deploy but if the vehicle has dual stage air bags the stages may not work correctly. If the passenger is there but is unbuckled the vehicle deploys both stages by default. If the vehicle does not know that the passenger is unbuckled, it may only deploy a single stage (not the end of the world).
It may also meant that something is wrong with the passenger present system. This may cause the air bag not to deploy.
Further diagnostics is required.