Propagation maps are looking bleak between Europe and North America. That said, actual results have been good between about 2200 and 0300+ (I'm not sure about the end time because I haven't seen loggings past this time).
I used the VOA propagation models at http://www.voacap.com/. The images depicted here all come from that site. Feel free to go to the site and check propagation for your region. For transmission power and mode, I used 100 watts of SSB because that seems like a pretty standard baseline for North American pirates & for at least some of the European pirates who might want to be testing specifically to reach across continents.
For the first image, I used Harrisburg, PA, as the location because it's the closest one to my location and that way no one will feel like I'm giving away their location. Here is 100 watts into a dipole about 30 feet above the ground on 14.1 MHz (essentially the same for either 13900-13950 kHz or 15010-15090 kHz).
Next up, the same specs, except at 2100 UTC:
Now, I'll switch over to Europe. I picked Netherlands because it's the hotbed of activity in Europe. Here's 100 watts SSB into an antenna about 30 feet high at 0000 UTC:
Now, to see what happens when the frequency drops. Here are the same variables but on 5.3 MHz (think just below 49 meters):
For about the past two decades, the primetime tests for Dutch stations who want to be heard in North America are about 15030-15080 kHz between about 1500 and 1600 UTC. Here's the same test except with the transmitter on 14.1 MHz (roughly the same) at 1500 UTC:
Even though propagation looks challenging, it appears that propagation will allow plenty of opportunities to hear stations in different parts of the world.