是否可以使用phpmailer中的gmails的smtp从yahoo的电子邮件地址发送电子邮件

<?php

require ("PHPMailer-master/PHPMailerAutoload.php");

$mail = new PHPMailer;

if(isset($_POST['submit']))
{
    $email_query = "select email1,email2 from tbl_contacts where id = '1'";
    $query_result = mysql_query($email_query);
    $value = mysql_fetch_array($query_result);
    $primary_email = $value['email1'];
    $CC = $value['email2']; 

    $name = $_POST['name'];
    $email = $_POST['email'];
    $subject = $_POST['subject'];
    $message = $_POST['message'];
    $mail->IsSendmail();                                      // Set mailer to use SMTP
    $mail->Host = "smtp.google.com";  // Specify main and backup SMTP servers
    $mail->SMTPAuth = true;                               // Enable SMTP authentication
    $mail->Username = $email;                 // SMTP username
    //$mail->Password = 'password';                           // SMTP password
    $mail->SMTPSecure = 'ssl';                            // Enable TLS encryption, `ssl` also accepted
    $mail->Port = 465;                                    // TCP port to connect to

    $mail->setFrom($email, $name);
    //$mail->addAddress('joe@example.net', 'Joe User');     // Add a recipient
    $mail->addAddress($primary_email);               // Name is optional
    $mail->addReplyTo($email, '');
    $mail->addCC($CC);
    //$mail->addBCC('bcc@example.com');

    //$mail->addAttachment('/var/tmp/file.tar.gz');         // Add attachments
    //$mail->addAttachment('/tmp/image.jpg', 'new.jpg');    // Optional name
    $mail->isHTML(true);                                  // Set email format to HTML

    $mail->Subject = $subject;
    $mail->Body    = $message;
    $mail->AltBody = $message;

    if(!$mail->send()) {
        echo 'Message could not be sent.';
        echo 'Mailer Error: ' . $mail->ErrorInfo;
    } else {
        echo 'Message has been sent';
        redirect('/contact.php?message=Your+Message+Has+Been+Sent!', 'location');
    }
}
?>

I am using gmail's smtp and it works fine if I send an email with a gmail account but when I send an email with an yahoo account it displays a success message but the message does not get delivered. Is it possible to send email from yahoo's email using gmail' smtp? If yes, how can I do it? And if not, how can I solve the problem?

In general,

avoid declaring incorrect identity.

This might be possible from technical aspect; however in 2016 most email systems tend to protect themself by using multip. techniques - like SPF, DKIM and DMARC and that is both for sending and evaluating received emails.

If this is true for more and more email systems and ESP's it's not hard to imagine what ESP giants like Yahoo, GMAIL and others are doing to express their hate on incorrectly declared identities (mark as spam, reject at SMTP handshake level, silently discard...).

In your case displaying success message only mean that your mail is received on MTA side for further processing, not anything about it's future.