If I restore my android phone to factory status will I loose my contacts (phone numbers)?

You don't need to reset it to factory default if WiFi is the only issue here. Just go to your phone settings, wireless, find your WiFi network and setup password again. But, if you want to reset phone to factory default, your contacts will be retrieved again as soon as you login with your gmail credentials to your freshly setup phone. To check if your contacts are in sync with your gmail account contact list, go to your gmail account and check out contacts. If you can see all of your contacts then you're ready to go, reset phone to factory default and starts again. If not, make sure to sync contacts with your phone gmail account before reset.