From my own viewpoint that would depend on how much daylight, and which SW band you're talking about.
I've heard 40 meter band hams and 41 meter band SW broadcast stations from SE Asia here in the NW US when it's daylight here, and obviously dark in Asia. Usually they fade out about two hours or so into daylight here, depending on overall SW conditions. A lot of what I just described could be what they call "grey line propagation".
With pirates that could be more of a problem, because they are much lower power than the stations I'm referring to. But I'm just saying it's still a possibility. Most of the SW pirates I am aware of seem to use the band just below 7000 khz., and propagation would be similar.
As far as hearing pirate SW stations, I've heard maybe 2 or 3 broadcasts just below the 40 meter ham band, and when I've heard them it was early evening, Pacific time. I think at least once I heard them during the weeknights. FYI I just use a 25 ft wire and a portable digital SW radio for SW.