No. Formitor's synthetic submissions are designed never to reach your real recipients. On each test, the spoke plugin intercepts the form notification and either suppresses it or redirects it to your monitoring inbox, and as of plugin v0.2.13 it also strips any To/Cc/Bcc the form itself configured, so even a client address sitting in a notification's Bcc cannot receive the test message. If you run an older plugin version, update to v0.2.13 (Plugins screen → Check for updates → Update now). Only the form's primary recipient was protected before v0.2.13; Cc/Bcc recipients are protected from v0.2.13 on. (As of plugin v0.2.14 this also covers Gravity Forms, which sends its notifications asynchronously on a background request.)
As of plugin version 0.2.57, each test submission also fills the form's email field with a one-time address such as monitor+run123@formitor.test. CRM integrations that reject duplicate contacts treat every check as a new contact, so a repeated test can no longer break the form's action chain.