Yes you can. This will require some custom coding on your end.
You will need to create a function which is called when a certain action is performed or a hook is 'reached'.
You need to make use of the wp_mail() function, which is a WordPress action.
Example
function b3_custom_mail_function( $to ) {
$to = 'email@recipient.com';
$from_name = 'Dummy';
$from_email = 'Dummy';
$subject = __( 'Your subject', 'your-textdomain' );
$custom_message = __( 'Your own message', 'your-textdomain' );
$custom_message = b3_replace_template_styling( $custom_message );
$custom_message = strtr( $custom_message, b3_replace_email_vars( [] ) );
$custom_message = htmlspecialchars_decode( stripslashes( $custom_message ) );
$headers = array(
'From: ' . $from_name . ' <' . $from_email . '>',
'Content-Type: text/html; charset=UTF-8',
);
wp_mail( $to, $subject, $custom_message, $headers );
}
Note
As you can see 2 values are defined as 'Dummy'. Why is this ? Because we're using a filter which overrides the sender name and sender email, just before the email is sent, to make sure you always have the correct sender name and email (to avoid spam).