5v/1A input instead of 3.6V/900mA input
It very well could fry. It depends...

If the battery output was put through a voltage regulator before the rest of the board, then your 5V will be converted anyway. If not, then you risk damaging lesser voltage components. Sometimes they fail slowly. 

Try following the traces from the battery input pin and see where it goes.

There is also the concern of the board expecting a battery on those pins, which is now a USB supply. If anything, it should shut down the board, because 5V from that battery would mean the battery is failing in a dangerous fashion. Since you say it works, then I would reckon there is no issue there. 

Because the standard USB power input port is gone, there is no risk of the bard trying to charge a battery on the battery pins.