No, the voltage across all LEDs would be the same as they're in parallell, but since LEDs are highly non-linear devices, how much current each draws might vary considerably due to quite small differences in forward voltage.

Say that the LEDs total current consumption and the resistor causes the voltage across the LEDs to be 2.0V. We aimed for a target current through the LEDs of 10mA each, but one LED might only draw 5mA due to it having a slightly higher forward voltage, while another might draw 20mA due to it having a slightly lower forward voltage...

/Michael