504 Error, Post SMTP at stake?

Hi,
Our new site is online since a few days, it has around 2000 users and a forum (Wpforo plugin).
At the moment, every time a message is published on the forum, hundreds of notification emails are send to the users, through POST SMTP and our provider’s SMTP server.

The sending seems to be OK, … but almost every time a message is published on the forum, the time to validate it is VERY long, and a “504 Gateway timeout” error occurs.

Would it be possible that the time needed for Post SMTP to send all these notification emails be the cause of this error?

Thanks for your help!