Can I replace a PLL Charge Pump with an Active LPF?
You definitely do not need a charge pump integrator for this application although you could use one if you wished.  The point of the charge pump is to integrate the output of the frequency/phase detector is a pulse oriented manor.  I don't think you need this level of complexity for what it sounds your trying to do so I wouldn't do it. 

I also highly doubt you need an active filter.  

If your only measuring at 1Hz then your averaging time is likely of a similar order.  

That is you don't need "fast averaging".  This means your low pass filter can get away with a very low corner frequency, 10-100Hz maybe 1kHz max?  

This is almost the exact opposite use case that the integrated charge pump is made for, which is converting the pulse train to a voltage to drive a VCO at as close to "full speed" as possible. 

With a corner frequency as low you need, you can likely just use an LC filter and the rejection at the switching frequency of this device will be extremely high as it appears that the majority of the frequency content in the output will be between ~200Mhz and 6Ghz.

You may need an op amp or two after this filter to provide gain / fix impedance issues for your ADC but the high frequency content of the signal should be low enough that you don't need a very high bandwidth op amp for this.

One issue you do need to consider is the input impedance of the LC filter.  You'll need to take it into account when deciding how to treat the transmission line between the filter(s) and the IC.

EDIT: I have no idea how sensitive your ADC is to high frequency noise but to effectively filter the very high frequency content that will exist in the output of the frequency detector you need to pay attention to the high frequency performance of your filter as PCB and package parasitics are significant at these frequencies.