Insurance is all about risk asessment and it stands to reason that if the company isn't aware of all the facts, they will give you a lower premium than if they knew that you had points/disqualifications previously. When you take out a policy on-line, the insurance is issued on the understanding that the information provided is accurate and true. If at a later date the insurance company discover that when the policy was incepted, facts were omitted - deliberately or not - they are perfectly entitled to cancel the policy back to inception, refunding any premium made and it is as tho the policy has never existed.
And yes Bond-007, insurance companies do have access to a database.
Blackberet28 - if it was me, I'd be honest about previous insurance problems, mainly to stop it biting me in the bum at a later date! It is quite possible that the company would never discover your history BUT is it worth the risk?