the method of connecting to the smtp server makes no difference.
It is the specific SMTP server that is being used to relay the email.
"whereas an email sent from a computer using the same address would use Google's SMTP settings."
only if you use Gmail as your mailing client.
it is possible to use the gmail smtp server for sending emails if you use the Pear Mail for SMTP mail object.
you need to enable authentication, use your gmail address and password as the username / password.
set the smtp server to:
ssl://smtp.gmail.com and use port 465