Update (2020-04-21) (mirror):
Foreigners whose visas had expired since March 26 will be permitted to stay until July 31 without having to apply for an extension, said Narumon Pinyosinwat, spokeswoman for the Thai government.
Official source: https://www.thaigov.go.th/news/contents/details/29468 (mirror).
Yes, according to the following sources.
Those foreigners who entered the country before the ban was imposed - who had visas, received visas on arrival or under visa waiver programmes - will not need to line up at often crowded immigration centres around the country to extend their stay.
The automatic visa extension has been granted until April 30, according to an interior ministry document. Police Lieutenant General Sompong Chingduang told Reuters the government could extend this deadline each month.
https://immigration.go.th/content/visa_auto_extension (now updated with English version of the image):
Unofficial translation of the official "Notification of the Ministry of Interior" on the "Permission for Certain Groups of Aliens to Remain in the Kingdom as a Special Case" from http://mfa.go.th/main/contents/files/news3-20200410-172909-334229.pdf: