Assuming the "WiFi administrator" only has access to the network, and isn't actively trying to attack you, I think your email is safe if properly configured.
Because they control the network, they can see all the traffic that crosses it. This would be a problem for unencrypted connections (e.g. HTTP traffic, or unencrypted POP or SMTP traffic).
However, the Google Apps Sync for Microsoft Outlook plugin specifies port 443 needs to be open for communications, and port 80 needs to be open so it can receive a certificate revocation list. This strongly indicates that TLS or some similar form of certificate based encryption is in use.
If you're using IMAP/POP/SMTP settings instead, the help page indicates that they can be configured to use encryption.
Incoming Mail (IMAP) Server - Requires SSL
Outgoing Mail (SMTP) Server - Requires TLS
Port: 465 or 587
Requires SSL: Yes
Requires authentication: Yes
Use same settings as incoming mail server
Therefore, if you have configured Outlook properly on your computers, the WiFi administrator won't be able to see your email content or recipients. They can only see encrypted blobs (essentially random noise).