At my work there is secure WiFi for all the employees. If someone has sent harrassment / sexual harrassment emails to me through the company WiFi, is there a way for my company to trace the IP address to their computer?
Usually you find the IP address an email was sent from in the email headers. Keep in mind that it is possible for the sender to forge this information, but a non tech-savvy person might not know how to do this. Unfortunately Gmail removes this information when using the web interface.
When your LAN uses a proxy server which logs website requests, you could check which IP addresses accessed gmail.com when the email was sent. Gmail always uses encryption, so you will not be able to find their username or even cleartext emails, just proof that gmail.com was visited from their device at that time.
Does your LAN use static or dynamic IP assignment (DHCP)? With static allocation your IT department should know which IP belongs to which device. But with dynamic allocation the IP won't be of much value because every device gets a random IP address whenever it connects to the network. When the DHCP server is logging its IP leases, it might at least be possible to find out the MAC address of the device which had the IP address in that timeframe. When you have access to a limited number of devices which could be the culprit, you could check if one has a MAC address which matches.
A tech-savvy user can also change a MAC address of a device, though.
What if my company files a complaint to Google (the person used Gmail) and they comply with giving whatever information they have on the account?
Google will only share private information when required to do so by law. That means you will have to file charges with your local law enforcement system and they will likely have to get permission by a judge to request the data. When sexual harassment is a serious crime in your part of the world, it might be possible to get a court order. When you need further advise about how to approach this, ask a local lawyer.