There is no question that the game handles FA bids in-game just fine. If the game only accepted the first bid, lots and lots of people would notice this and it would have been fixed a long time ago.
I have personally tested this at length. It works fine.
Now, if you want to assert that the first bid made of two identical bids has an advantage ... that may be the case. The first bid for certain doesn't always win, but it may have a leg up. I haven't seen enough data to confirm this.
However, if you're entering bids manually, the first bid entered would get the same advantage.
