Immobiliser will still allow pump prime and the car to turn over/ act like normal. It will only cut the injectors and spark. I had a big issue with immobiliser.
However, how you'd go about fixing it I am not sure. It could have glitched out and confused when you pulled the plugs.
To reset everything, your best option is to pull the positive cables from the battery, as some things have their own earthing and pulling wary cable may not always reset things.