No, it wont
Depending on voltage applied, LEDs pass through certain amount of current. In 485p case at 1.1V LEDs passes 0.001A, at 1.5V it passes 100mA, at 4V it "passes" 2A.
Resistor shows voltage drop across itself. Resistor is "current limiter" in sort-of-speak meaning. But, when you try to calculate values in this circuit, resistor as "current limiter" is way to go.
Battery can give maximum voltage of 1.5V. It is safe to have no R in this case (LEDs with V forward at 1.5V).
With unregulated (even with some regulated, poorly though) PS you could have problem.