No, it´s not as simple as that.
The owner of a vehicle is liable for both insuring the vehicle and making sure it has valid MOT / ITV.
Vehicle insurance and the responsibilities of an insurer once a policy has been contracted for a vehicle, are a separate issue from the obligation of a vehicle owner to make sure the vehicle has valid MOT or ITV. But, not meeting that obligation, can have serious consequences.
The law on exemptions from the ITV even with vehicles parked on private parking or areas:
“Article 3. For the exemption of the mandatory inspection due to the non-use of the vehicle on public roads, it will be necessary to obtain the temporary discharge of the vehicle at the Provincial or Local Traffic Headquarters corresponding to its entry in the Vehicle Registry , Who will communicate this circumstance to the competent organ of the Autonomous Community of the place of registration”.
The most common third party vehicle insurance will pay out if you are involved in an accident and found the guilty party. The policy is valid. BUT, as you did not meet your obligation, under Traffic Law to make sure the vehicle has valid MOT or ITV, the insurance company is entitled to re-claim the damages paid to the third partyfrom you, the policy holder.
To stress, obtaining an ITV certificate for a vehicle that is not on Spanish plates, does NOT protect you from this risk as it will not meet the traffic regulations.
The same can be said if you are found to be driving under the influence of alcohol, the insurance company is obliged to pay third party damages but, will claim cost back from you the policy holder. Due to the fact that you did not meet the obligation to be a responsible driver under the traffic Law if you were driving under the influence.