We had sex between August 27th - 31st 2013, Girlfriend says Sonar scan reveals due date as 15th May, is this possible?

You mean Sonagram, Sonar is what ships and submarines use.

The doctors guess will be accurate to plus or minus 2 weeks meaning effectively the entire month of May not just that specific day. That is nine months so yes it is possible.

Certainly its possible. Doctors generally calculate a due date as 280 days from the onset of their last period, which is 40 weeks. But that estimate can be off by as much as 5 weeks, depending on whether the woman is sure when they started their last period and other factors. Calculating a due date is an inexact science as is calculating a conception date. A May 15th due date means that conception occurred sometime within a period of 8/15 -9/15. So yes, its possible.

If you are concerned whether the child is yours or not, the only way to confirm it is with a DNA test after the child is born.

The doctor calculates pregnancy according to her last monthly period (LMP) not by when you had sex. So, yes, it is entirely possible.