It's possible but it depends on how the Fiat immobiliser works. The Cobra immobiliser section seems to be hooked into the Key Code Unit, probably in series with the sensing coil, because if I don't disarm it before turning on the ignition the 'Code' warning light comes on. However it doesn't come on when the engine cuts out. It happened again last weekend and I managed to restart it, by declutching and using the starter, whilst still rolling.
I would have thought, from a safety standpoint, that the Fiat immobiliser would only check the code at start-up and not whilst the engine is running (to avoid the exact situation I'm currently suffering from) so that would mean the Cobra couldn't cause the problem.
The problem seems too random to be a faulty pump seal. I'll be taking it on holiday next month when it will probably cover over 1000 miles and I've also started using Millers in the fuel so it will be interesting to see if it gets any better, or worse, with regular use. Once I get back I've arranged for the dealer to have it for an extended period so he can see the fault for himself. Watch this space!