Hi @joss,
With BuddyPress, you can create new emails by going in Emails > Add New. Then on the left side, in the “Situation” panel, you can check the “Recipient has registered for an account.” box. Then in the text editor you can write your confirmation email and save it. With these settings, that email should be sent when a user registers on your site.
However, please note it’s possible that the BP Disable Activation Reloaded plugin blocks all emails sent on user registration. If that is the case, then unfortunately I believe there is no easy way to send a confirmation email because that plugin will just block the emails.
Hope this information helps.
Best regards,