--- and closely space parallel are considered a single runway for spacing?
underfire,
Certainly, in this case, and other I know in US, the answer is no. On a visual approach ATC is not providing separation.
If it becomes IMC, movement rates, of course, drop, and the whole exercise becomes a tad more complicated, but still always works well.
Given considerable disparity in approach Vref. speeds and actual profiles, it is common to overtake or be overtaken.
Have a look at the lateral spacing of the runways at KLAX, and it is operationally possible to have aircraft in parallel on approach on all four runways. If you want to find a case of seriously "up close and personal" try John Wayne International, although the length of one runway does limit the size of aircraft using it.