It is dealt by calibration which requires having a good characterization of the filter, as Stanley mentioned.
You asked about isolation:
There are different implementations of how saturation is avoided during transmission in pulse-Doppler radar, however they virtually all involve physically isolating the receiver. The time while transmitting is your effective pulse width.
There's the additional time of filtering the received pulse. Here is where the filter must be taken into account for measuring range: the pulse width and this extra processing time from the filter determine the minimum measurable range, called the blind range. Many times the filter processing time is much less than your pulse width and does not contribute to the blind range significantly. This is less the case when you have slower processors and shorter pulse widths, where the filtering processing time can be well within the order of your pulse with.