I think the answer's probably generally not unless they ask you, or you give them permission one way or another (ie by providing references/history on a resume, or as a condition of the job).
I think beyond that there'd be some pretty major privacy concerns... once upon a time they wanted an "Australia Card", where all sorts of public bits and pieces (drivers license, TFN, etc..? don't knw what exactly, but that sorta stuff) would go onto the one card with one identifying number, etc. The idea was convenience, I believe, rather than having 50 different numbers and cards and accounts. However, it was knocked back due to the concerns some people raised about privacy.
SO, what I'm saying, is that if there are privacy concerns about something as 'simple' as making something more convenient, there'd not be any central databases, etc, that they can look up without asking/telling you. I'm a Scout leader, and they had to tell me (I had to sign a form to give permission) to let them do a criminal background check on me. From there, when you get a credit card, they're not allowed to do credit checks on you unless you've got that little box ticked saying you give them permission to...
....nothing unless you say so. (That mini-thesis is understanding, anyway!)