The only problem I see is if (after a serious incident) the logbooks are looked at and the non-insured pilot is shown as having booked the hours in a number of previous flights. This could happen with either the CAA or the insurance company
A one-off is a different matter.
I was always given the example of the Graham Hill crash where the insurers failed to pay out. I'd be interested to see if they pay out on the Colin Montgomery crash given that his licence appears to have expired