Can you approximately detect the closure of up to 100,000 switches using a resistor chain?
Could it work? Sure. At 10 GHz, exactly as designed? Not really. The main problem is that it takes time for changes to propagate down the wire. If you want to run at 10 GHz, that wire will have to be very short, only a couple of cm maximum. Not to mention that you would have to wait some time for things to settle down to 1 part in 100,000, or however accurately you intend to estimate the count. However, there may be a way to do something similar that could work at that speed by breaking it up into multiple stages, albeit it would certainly have more than 100 ps of latency.