SE accounts are per person, not per company and as far as any of us care, its ethical. In theory, the only situation where this would matter is if you're representing the company in some official capacity, and that's sticky on its own. As long as the two accounts have been totally separate, its probably fine.
If the account is something your company asked you to create in an official capacity - in theory, they can't/are not supposed to use the account (since an account is a person) and ought to retire it.
I personally wouldn't recommend using a work email address (especially a google account) as the only login on an account through, depending on your workplace, since there's every possibility your account could get deleted before you could change the login method . (I wouldn't use it for anything either, but I've been through a few jobs so... unless it absolutely was official, I wouldn't bother).
So, as far as how we do things? Its probably entirely fine.