My Cousin is a president of a PTO and needs to send out up to 700 emails at a time to parents. Will Gmail allow that many emails to be sent out at one time?

http://help.google.com

Sending limits
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In an effort to fight spam and prevent abuse, Google will temporarily disable your account if you send a message to more than 500 recipients or if you send a large number of undeliverable messages. If you use a POP or IMAP client (Microsoft Outlook or Apple Mail, e.g.), you may only send a message to 100 people at a time. Your account should be re-enabled within 24 hours.

If you communicate with the same group of people on a regular basis, you might be interested in Google Groups.

If you send a large number of undeliverable messages, we suggest verifying your contacts' email addresses. It's also important that everyone you are sending mail to is willing to receive it.

Learn more about best practices for sending a large amount of mail through Gmail.