Can you predict how long a discontinuity will take to reach its target if it is low pass filtered at a certain frequency?
Infinitely long. It's an exponential decay, so it never goes back to 0. 

The time constant for a 200 Hz filter is $\frac{1}{2 \pi f} \approx 0.8ms $. About every 0.8ms it drops by about $2/3$ or every 1.84 ms it drops by a factor of 10.

If you define "almost zero" as one millionths you need to wait $6*1.8ms$ or about 11ms.