This is now a provision. According to Greek immigration law, the Greek embassy can check you, but if your status is not considered dangerous to the country, it will be OK.
What is the due-diligence process like for Golden Visa applicants?
I was convicted of a felony in my home country and served one year in jail. However, it has been a decade since that time and I have had no criminal wrongdoing since. Am I eligible for the visa for me and my family?
An entry visa - that is, legal entry into the country - is necessary to obtain a resident permit for owners of real estate property. A criminal record certificate is not needed for the completion of the Golden Visa application. But for issuance of the entry visa in your country, Greek embassies may ask for a clean criminal records certificate. After you legally enter Greece, it is not needed to submit such documents for your Golden Visa application.
You are eligible for a Golden Visa since there is no due diligence on criminal records. You just need to make sure that a tourist visa will be granted by the Greek consulate of your country in order to be able to visit the country the first time. You do need a first entry into Greece to start the Golden Visa process.