Yes, can get the date the image was shot with the below code. You would then create a new text layer, position it where you want it and use the return value of the below function to replace the text content.
function getEXIFDate(){ var eDate = false; for(i=0;i<docRef.info.exif.length;i++){ if(docRef.info.exif[i][0] == 'Date Time Original'){ eDate = new Array() eDate = docRef.info.exif[i][1].split(' ') };//get the date from the exif file returns false in it does not exist. };//end for loop to get EXIF date return eDate };//end function getEXIFDate