*Im not a lawyer or an insurance expert
But
Some insurers will complain if theres a keyless issue theft but if your policy states the car has the standard alarm and immobiliser and you followed manufacturer instructions they really dont have much of a case except to not insure you in the first place or contact you and nullify the cover when they learn of shortcomings.
If you have a valid policy then yes they should pay assuming you have theft cover (e.g. not just third party cover or cover via a comprehensive policy but the car that gets stolen isnt yours or some other circumstance)
If youre covered youre on the hook for your agreed excess and they should pay out - NB they will pay the
current value of the car in most cases, hence why gap insurance exists.
Thats in the UK, in other countries I dont know. Once again Im not an expert so if in doubt contact your insurer.

Ed