Note: You have to follow these steps, just uploading an emf to Google Drive doesn't work

Upload the target SVG file to Google Drive, as a regular file.
Install "CloudConvert" into Google Drive, and give it permission to read all your documents (scary!
Click on the SVG file, and right click to send to CloudConvert.
Convert to "EMF" format and (this is crucial) save back to Google Drive.
Open the EMF in Google Drawings and verify it looks good.
Under the Edit Menu, choose Copy.
Finally, in your Google Doc, choose Paste.