I actually checked that and it looks like they have implemented their own class from scratch. The structure is similar to wp_mail(), but, as far as I could find, wp_mail() itself is not used anywhere. It is late here now, but I can post the relevant file names etc here tomorrow.
As for configuration, I use postfix on a Digital Ocean Ubuntu 16.04 droplet, no SMTP plugin (yet, anyway) and every other email sent from WP logs beautifully with your plugin.
I will also test adding a line with bp_email() filter in your plugin where you have all the other filters and let you know what happens.
Having this exact same problem after last ACF update, and had to temporarily disable MLA (the entire site is built around ACF, so disabling that was not an option). When do you think the next updated version of MLA will be released?