Absolutely! To share a specific email account with other team members in your organization, you can change the permissions for "Who can send emails from this account" from 'Only Me' to 'All team members'.
To change the settings go to 'Connect My Mail' found in Settings.
Find the email account you want to share and click the edit button.
Scroll down to the section titled "Access Information". You'll find this section on the bottom of the connected email accounts settings screen when you connect a new email account.
Adjust the radio button for "Who can send emails from this account" from 'Only Me' to 'All team members'. Click Save to finish.
If you don't have the account setup click Add Email Account. To start adding email accounts and to allow sharing see "How do I Connect My Email in my account?