I would think if you have voltage at the coil and the engine turns over it wouldn't be immobiliser.
I had a problem similar to this recently and it turned out to be a duff battery. The voltage at the coil dropped to 7v in my case and the spark, when I got one, was yellow and as weak as piss. In the old days a 6 volt coil was fitted with a dropper resistance in series which was shorted when the starter was opperated to effectively put 12 volts onto a 6 volt coil.
I don't know if the digi has this, I bloody well should know, as I've had these now for 21 years. I suspect not, but someone on here will surely know.
Anyway, good luck with it, as I know, it can be a ball ache.