No, you are not eligible to receive any gratuity unless you complete 5 years.
Gratuity Calculation Considerations
Now, what you have cited—the 4 years and 240 days or half fraction yielding to more than 6 months—is only taken into consideration for the payment and calculation of gratuity.
240 days in the last year are only taken into consideration if you are in the jurisdiction of Tamil Nadu.
Employer's Discretion and Legal Binding
Now, it rests on the employer's wish. Some employers consider the 240 days in the last year, and some don't, as the verdict was given by the Madras High Court, and it's binding upon Tamil Nadu region employees. So legally, if you are not from the Tamil Nadu region, your employer can well decline to give you the gratuity benefits unless you complete 5 years of employment service.