It would probably oscillate with no input. The LEDs will have capacitance, so it could lead to high frequency oscillation.
With a 3 V supply, the input threshold voltage would be around 1.5 V. The input could sit a bit below that, so the output is high, without any current flowing in the LED, so it might be stable in that condition.
Also, with no input connection, the LEDs may generate voltage from ambient light, so the behaviour may depend on the ambient lighting.
I would suggest that you put another inverter between the DUT and PL1, and then you can put a high value resistor between the input and ground to stop it oscillation if the DUT is open.