An email that arrives through this channel shows up in your Conversations inbox just like a WhatsApp or a Telegram one: you can read it, take control and reply from there. When someone on your team replies manually from Conversations, that reply goes out through the same connected mailbox (same SMTP server, same sender address) — the customer receives it in their inbox as one more email in that conversation, without the AI notice (that notice is only for replies the agent generates).
The full detail of reading, taking control of, replying to and resolving a conversation — valid for any channel, Email included — is in Manual 16 · Conversations.