Yes. EasyEDA can work under offline. but you need to save your design to locally.

To save designs locally: Document > EasyEDA Source then click in the text area of the window that opens and do: CTRL+A CTRL+C and paste (CTRL+V) into a text editor. Save the resultant text file with a name of your choice. To load this file back into EasyEDA, open a new EasyEDA editor canvas of the appropriate type. Next, open a new EasyEDA Source window and paste the contents of the saved file into it and then click Apply. The file then reappears in the EasyEDA editor window.