Technically possible ? "Yes" but practically not :-(
Firstly, the employee card won't have any personal information on it - it'll just be a manufacturer ID + serial number. You'll have to source the employee information yourself. An API into the door access mechanism? Very unlikely unless you are on very good terms with the supplier ... Good luck getting past your in-house security team - or even worse - the landlords. Remember these are not technical people and they'll start thinking API = Tom Cruise + Mission Impossible hackers !! Even getting "just" a csv export of employee + ID number from the system may be unobtainable.
Secondly, even if it were possible to encode personal data onto the card (eg the ePassport type), these are only unlocked by supplying certain credentials to "prove" you have the passport in your possession (which is passport number, DOB and expiry date).
If you just wanted a show and tell then you could see if one of the generic NFC reader apps recognises and reads the serial ID and then just go through a slow process of collecting that data yourself.. Obviously when people leave / join / lose their card etc etc you'll have your work cut out for you.
I've done a bit of work with the Android NFC examples (in the SDK). They're not exactly great but they do work and the NFC API is good enough to work with - at least read the public bits etc etc.