CML signal to ground terminated line or peak sensing ADC for short pulse
A CML driver will have no problem with driving an AC-coupled line. After AC-coupling you can terminate the line to any dc voltage you like. A bias tee is likely not necessary --- a simple 50 ohms to whatever voltage suits the receiver should be fine.
If you do want to use a bias tee for some reason you haven't revealed, it's a linear device, so it won't cause any distortions. It will act as a (very wide-band) bandpass filter, so you may need to look out for those effects.
When you ac-couple a low duty-cycle pulse signal, you are likely to see an effect where changes in the duty cycle cause the base level of the signal to shift. That could affect your peak voltage measurement.
Your ADN2880 amplifier has only 2.5 GHz bandwidth, but you're trying to measure a 200 ps pulse. This means the pulse has frequency content into the range where the amplifier response is starting to roll off. Changes in pulse width or drift in the amplifier bandwidth are likely to affect the peak voltage measurement.
You can probably make a peak detect circuit effective at these frequencies with an rf diode of some kind, but I don't have any part to recommend off the top of my head.