I sympathise. Insurance costs for young drivers is spectacularly high and I did pretty much what you did when I was a teenager. However after being 'rear-ended' my solicitor advised me that I was committing fraud and that I should arrange my own insurance. I did, and umpteen years later (and with very cheap insurance costs) I have never regretted that advice.
Talk to DVLA. For a government department they are terrific to deal with and have excellent customer service advisors. They will in all likelihood know you have penalty points. Furthermore, even if they don't (but you, of course, do), you have a 'fiduciary duty' (a duty of good faith) towards your insurers.
In the event of an accident you could find yourself in some real serious trouble if the insurer finds out that you have been economic with the truth. The least of your worries would be that the insurance company would refuse to meet any claim you made against the policy. But you could also be charged again with having no insurance, fraud, and you can forget about finding a company who will insure you again.
Don't take shortcuts to circumvent or avoid doing the right thing. It will work out best for you (as it did for me) in the longer term.