Can I take a loan to purchase property to be used toward obtaining a Greek Golden Visa

This is a no-way option of obtaining a Greek Golden Visa. The motivation is supposed to be offered when you produce the amount of money needed from a foreign source that's outside the Greek economic institutions.

Sure, you may receive a loan so as to purchase a property with Golden Visa process. You will need to seek advice from a local bank branch for that.

According to the relevant provisions οf Greek immigration law in force, the investor must have full ownership and possession of the property at the time of submitting the permanent resident application, and the existence of a mortgage constitutes an obstacle to this condition. The submitted documents from Land Registry have to prove that the property has no encumbrances, mortgages, etc. After the issuance of a resident permit, the investor may obtain a loan in Greece or anywhere else, with a mortgage on the acquired property, under the related terms and conditions of each bank. In all cases, the price of the real estate has to be paid via a crossed bank check or through a banking transaction from the Greek bank account of the buyer to the Greek bank account of the seller. So a loan can be taken only from your domestic bank, provided that no encumbrances, hypothecs, etc., are on the under acquisition property. If your domestic bank could provide you a loan with securities beyond the under purchase property, there is no obstacle for the Golden Visa procedure.

Funds must be transferred in a bank account (yours or the seller's directly) from a bank based outside Greece. If you succeed to get a bank loan, then yes, you are still eligible for the Golden Visa. But it is very difficult to find a loan from a Greek bank based abroad.

To my knowledge, the banks do not offer mortgages to foreign investors. And kindly note that to be eligible for the Golden Visa you will need to complete full payment of 250,000 euros. Until full and final settlement of all mortgage payments, you will not be able to apply for the Golden Visa. 

I believe that such a possibility does not fall within the scope of the Greek law providing for the Golden Visa, which is to attract foreign funds in Greece. Besides, one of the documents that you have to submit to the competent Greek authority (Aliens and Migration Office) is a certificate of non-pending claims and obligations (i.e., that the property is not mortgaged/seized). I cannot imagine a Greek bank providing you a loan without a mortgage on the property you want to purchase.