Yes is the short answer. However it all depends on what type of defaults are unpaid and why they occurred. Remember, lenders who specialise in helping people with impaired credit are human, they understand that from time to time we are not going to be able to make all the repayments we've previously committed to.
WARNING: If you read this website, your chances of getting car finance with bad credit will dramatically improve.
Note: Unless you can now afford to meet all your commitments as well as a car repayment, no lender will be able to help you whether you have unpaid defaults or not.
Defaults whether paid or unpaid will often be individually assessed. Most lenders will overlook a gym membership default and often a telco or power bill (if it's less than $1,000). If the defaults (regarless of who they are to) are over $1,000 then you will need to make sure you have a good reason as to why and how they occurred. Generally, if you have a finance default you would be highly unlikely to be given another finance contract. But each default will be assessed separately and its own merit.
A lender may ask for you to put some money in to the car like a deposit. You could trade in your current car to the dealer who you are going to be purchasing your new car from. This gives you equity in the vehicle and means the financier will make the assumption that you are more credit worthy than someone who is unable to contribute anything to the purchase of the new car.
You can get a car loan with unpaid defaults but it will entirely depend on who they are with and the reason they have become a default on your credit file.