If they bought it from Apple (which is probably unlikely as most companies have contracts with the carriers individually), then they can just punch in the serial, find the receipt, and give you credit for the exchange in most cases. But if it was purchased from a carrier, then no... But the good news is they may be able to tell you where the iPhone was sold from (like AT&T, Verizon, etc)... and then you can try it over there.
Might be easier to go back to your purchaser or IT dept to see if they would allow you to upgrade by paying the difference, similar to when employees travel and pay the difference to extend their trips for personal vacation. However, since it's equipment, I can see them seeing an issue since they would worry who would actually own the phone in case of termination, etc.