I've got a new test install with BuddyPress and WPMU dashboard active (support access enabled). Other plugins are now off but I've tried Mailgun, and numerous SMTP plugins (with GSuite and Sendpulse accounts). I receive emails when clicking the test email button in the SMTP plugins. I do not receive emails when I sign up or go to Users > Manage Signups and click email to resend. Turning off BP, I then get emails for the regular WP signup.
When using built in WP mail sending via the host without any plugins, the receiving GSuite would complain about the low rep of the host IP and not deliver the msg. I think this occurred for both WP and BP, which lead to trying different sending servers. Unfortunately, I can't use BP if it doesn't send emails reliably.