It all depends on how much logging your company is doing on the network.
Odds are the public IP address that is captured by the blog host would be the router’s public IP. All users network traffic probably comes from this IP address. For the company to track this they’d need to track all network traffic through the router as well as what computers are issued which internal IP address, as well as what user was logged onto that computer at that time.
It is possible to track, if everything was setup in advance to make it happen.
It is possible.