Do we need PHPMailer?
You don't need PHPMailer. You will need an SMTP server of some description.

If your server is Linux, you will need to install some method of sending email such as postfix. You could either let the server distribute email itself, or configure postfix (or whatever) to relay it to another email server.

If it's Windows, I believe you can configure PHP to use an external SMTP server without needing one on the Drupal server itself.

If you were set on sending messages through Google's SMTP servers, you will probably want to use PHPMailer, as it's set up to make that sort of thing easy. Getting hold of your own SMTP server is not tremendously difficult, however.

Can you tell us more about your hosting environment? Maybe we could be more specific with the answer.