We are having the same problem…and here is the server information for us”
OS: Linux web 3.13.0-132-generic #181-Ubuntu SMP Wed Sep 13 13:25:03 UTC 2017 x86_64
PHP version: 7.0.23
WordPress version: 4.8.2
WordPress multisite: No
openssl: Available
allow_url_fopen: Enabled
stream_socket_client: Available
fsockopen: Available
cURL: Available
cURL Version: 7.45.0, OpenSSL/1.0.2l
It sounds like we are having the same issue. We are a Google G Suite Partner, and I have posted a case on this in the Google Connect for Work community at Has Anyone Solved API Error Issues For Gmail SMTP WordPress Plug In?.
We are using the same version server that you are. This has become a P1 level issue for us.