Yes, im pretty sure you can use FC from multiple IPs as long as your account is the only one to use FC on those IPs..
BUT you might want to think about the RISK you would be taking. If ANYONE else at your work ever logged into FC on their account, it would show up as you both logged in on the same IP, thus having 2 accounts linked to 1 IP, which more then likely would terminate both of your accounts. This is why FC reccomends not logging in on a public network, because if you log in at a public place, say a library, a coffe shop, a work place office, ect.. you have no guarentee that noone else hasnt already, or wont in the future, also log in to their own FC account..
If I was you I wouldnt risk it.