Using a CMOS 555 as a window comparator
If we look at the TLC555's internal block diagram:



We can see that the THRES input goes into a comparator which controls the Reset input of the flip-flop. So depending on how we connect THRES:


THRES = VDD: the flip-flop will continuously reset
THRES = GND: the flip-flop will never reset
THRES = the voltage across the timing capacitor: reset when the capacitor is charged to 2/3 * VDD


The most useful scenario is obviously the 3rd and that's also a typical usage case for this chip.

Never leave the THRES input floating as that indeed can lead to unexpected results and high quiescent power consumption! This is a CMOS chip and the THRES input is a very high impedance CMOS input so it must be connected to some well defined voltage.

In your application circuit, THRES is well defined by your RC circuit + MOSFET so in my opinion there should be no issue at all.