Is it possible to get accepted in a PhD program without reference/recommendation letters?
Most admissions committees I know people on will not consider incomplete applications. 

If there is an application deadline that applies for an entire incoming class, and letters aren't received, then it's probable that the application will be rejected. 

If there is no admissions deadline and If the rest of the application looks good, though, they may contact the applicant to remind them to send in letters so that the application can be considered. 

The reason for asking for the letters is a form of quality control: admissions committees want candidates who will become productive researchers. Getting letters of recommendation that can testify to their promise as researchers is an integral part of the admissions process.