No, they don't... unless you're a Nielsen family equipped with the digital equipment (People Meter) instead of the manual diary many still use.
My last full time job was as Director of Technology for Nielsen Entertainment, based in Hollywood. I'm pretty familiar with the issues, myths and technology around all this stuff.
We would have loved to get direct data for all cable households, but there are many problems with that approach. For one, we don't know the family size, ages, races, etc. for members in every household. Another big issue is that a lot of people are "cutting the cord" these days... now watching movies using Amazon, Netflix, etc. and watching stuff like the Oscars over the air... which offers no way to measure.
The networks understand the issues, and strongly resist efforts to more accurately measure actual viewership. The Nielsen families are inherently biased... usually being avid TV watchers (which is why they agreed to be Nielsen families in the first place). This over-inflates reality, and the networks are quite happy with that.
The networks supplement the Nielsen Family data with surveys, where we would sample other viewers via phone and web surveys, and use that data to "adjust" the diary data for the benefit of their advertisers. But still, the demographic data (age/race/income/geographic) are key when looking at and using the data for anything at all.
So I did not have to carefully avoid turning my TV on or past ABC, even for one second, so that they did not get credit by Nielsen? I always wondered about that.
Most people never shut off their cable box and the same channel is on when they are out of the house, sleeping or when the tv is shut off.