Can i submit new EAD application to California Service Center May 2020?

I am planning to submit H4-EAD (I-765) documents to the California Service Center

Are they still accepting EAD documents to mail this time or do I need to send after May 31st 2020?

There are not restrictions in place currently. You can send documents to all USCIS centers.
For your case too, you can send it.