Well, yEd does offer BPMN symbols and a BPMN layout algorithm. You could create the diagram structure manually and then use yEd's BPMN layout algorithm to arrange your diagram. However, yEd is not able to export to a BPMN specific format. You could try saving your manually created BPMN diagram as GraphML (yEd's native, XML-based file format) and then use XSLT to transform GraphML into a format supported by e.g. Camunda Modeler.
I think a much better approach would be using one of the yFiles programming libraries, though. (yEd is built upon the Java version of yFiles.) The yFiles libraries provide (high-level) APIs for creating, arranging, and visualizing graphs. The BPMN symbols used in yEd are included as source code demo with yFiles. And even though the yFiles libraries do not provide an export feature to a BPMN format out-of-the-box, it is possible to implement such a feature in a custom application.
The yFiles libraries are available for several platforms (HTML5, C#, and Java) and may be evaluted free-of-charge. I suggest to give yFiles a try.