GND pin of a RF device
The output doesn't contain frequencies as high as the 8GHz the input is rated for.
The output is the power level, not a copy of the input.
Transmitters don't change output power that fast, so your output won't change that fast either.
That said, the datasheet shows the detector responding to a change from no signal to -10dB in less than 20 nanoseconds:

You'll have to deal with sharp transitions there, but nothing worse than you would encounter in dealing with moderately fast digital signals.