As you should be aware whether you are a G, G1 or G2 holder it is illegal to operate a vehicle on the roadways of Ontario, Canada without the vehicle being properly insured. So, no with a G2 you cannot legally drive a vehicle without insurance on it. If you are going to drive any cars you should first make sure the vehicle has proper insurance on it and secondly that the insurance would cover you operating the car.
Ontario has compulsory automobile insurance. Before you can attach plates to a vehicle or renew your registration, or buy a temporary (trip) permit, the vehicle must be insured. In Ontario, private companies provide insurance coverage.
All vehicles must be insured for third party liability for at least $200,000. This covers the car owner in the event that they injure or kill someone or damage someone's property. Collision insurance to cover damage to your own vehicle is a good idea but not required by law.
When driving your own or someone else's vehicle, you must carry the pink liability insurance card for that particular vehicle. You must show this card when a police officer asks for it. If you do not, you can be fined up to $400.
Every person who operates a vehicle without insurance is guilty of an offence and is liable on a first conviction to a fine of not less than $5,000 and not more than $25,000. On a subsequent conviction can receive a fine of not less than $10,000 and not more than $50,000. Also if you are ticketed multiple times for driving without insurance there may also be jail time handed to you as a penalty.
As you can see driving without insurance is a serious violation of the law in Ontario and you would be handed quite harsh penalties if you are caught in an uninsured vehicle so we would suggest that you always make sure there is coverage on the car, that extends to you, while driving with your G2 license and when you progress to your full G driver's license.
It appears this costly fine would be placed upon you whether you owned the uninsured vehicle or was driving someone else's vehicle without insurance on it.