The airbag is activated by a simple g-meter... basically it goes off if you hit something that makes the car decellerate more than it could just using the brakes.
The rest of the car ought to be the same as the non-airbag version. I'm not sure that the Cinq/Seicento was ever so sophisticated that Fiat decided to re-engineer it extensively to add crash sensors, or make it more compatible with the airbag (sounds unlikely given the airbag technology at the time and the fact that the model was about to be replaced by the 500 soon anyway).
I also doubt that the airbag version had pre-tensioning seat-belts, which these days augment the airbag. If it had them, and you fit an airbag, then fit those too.
So I'm not sure it's the end of the world, if you fit an airbag. It's very unlikely to go off by accident since the g-meter controls it and it takes a hefty old shove that's likely going to hurt already, before the airbag is tripped.
You won't ever know for sure that it'll fire... you only need to miss one bit of wiring, or have a slightly moody g-meter for it to not work (which is why it's handy to have the light on the dashboard working) but it can't do any harm to have something that *might* work.
But it's probably better to just recognise the car is old tech' and about as strong as a wet cardboard box...and just take it a bit easy/avoid any trees/trucks and stay away from motorways.
If that bag ever fired, you're going to be in severe trouble... I can only think it might save your teeth. The rest of you will be fixed by the NHS for free.. but teeth are expensive.
Ralf S.