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Read the datasheet and do the math.

On page 3 of the datasheet we find that the guaranteed high and low threshold voltages for the PS/SYNC input are 1.4 and 0.4 V, and its maximum input current is 100 nA.

First, let's analyze your circuit letting the input float high.  Your lowest power input voltage is 3.0 V, which is 1.6 V above the min guaranteed logic high threshold.  The 1 MΩ pullup will therefore source at least 1.6 µA.  Subtracting the pin input leakage current leaves 1.5 µA of headroom.  I didn't look up the maximum leakage of a 2N2222 transistor with its base held at the same voltage as its emitter, but as long as it's somewhat less than 1.5 µA you are OK from a DC analysis point of view.  Whether there is sufficient margin to hold the pin high in a noisy environment is something you will have to decide.  A small capacitance to ground could help with that.

Now let's check your circuit driving the PS/SYNC pin low.  We can see just from inspection that the base current thru R2 is well more than enough to turn on Q1 to sink a few µA, so that's fine.  R3 guarantees Q1 is off even when the microcontroller output is high impedance.  I would put R3 on the right side of R2 (directly on the base of Q1) for better noise immunity, but your circuit should work as is.

The above is assuming you are only driving PS/SYNC for the PS function, not the SYNC function.  Your circuit is way too slow for the SYNC function.