No. If your company has made the Emails tool an active tab on your project (see Set the Active Tabs on a Project), your project's team can also send email messages directly to the Emails tool from their email client. All anyone needs to know is the project's 'Email into Procore' address. This is an inbound email address for the project's Emails tool, which can be added to the To and Cc fields of any email message.
To locate the email address:
If a user with 'Admin' level permission to the project's Emails tool has created a 'Default Distribution' list (see Configure Advanced Settings: Emails), members of the default distribution list will receive ALL emails that have either been created in or sent from the Emails tool. Members will also receive all messages sent to the Emails tool via the inbound email address. This includes emails that have been marked 'Private'.
For instructions, see Send an Email to a Project's Emails Tool.
Note: In addition to the Emails tool, other Procore tools have project-specific inbound email addresses that team members can also use to send messages. For details, on your options, see Where can I find the email address to send photos, documents, and emails to Procore?