It depends on how you choose to send the 1:1 email.
If you connected your email account to deals, then 1:1 emails will appear in the "Sent" folder. This is because these emails are sent from the connected email's server.
If you choose not to connect your email account, then 1:1 emails will not appear in the "Sent" folder. These emails are sent using ActiveCampaign's servers.