Unfortunately, no.
If there is a complete failure of title, you have no protection and would lose both your property and your equity in the property. The lender, because of their Lender's policy is the only one protected.
For example, let's say you purchase a piece of property in the amount of $100,000. The down payment on the loan is $20,000, leaving the loan amount at $80,000. However, your equity of $20,000 is not covered since you did not get an owner's policy. Now, what would happen is some matter arises affecting the past ownership of the property? The title insurance company will only defend and protect the interest of the lender because of the insurance of a loan policy. Your self as the owner would have to assume the financial burden of legal fees. If your defense proves to be unsuccessful, the result could be a total loss of title. The title insurance company would pay the lender's loss, and you as the borrower would lose your down payment and any other equity you may have accumulated of the property itself. Not to mention the amount you owe on the note if still due.