For future reference, here are the specs for the reconditioned HP Pavilion Power 580-137C Gaming Desktop being considered:
Processor: AMD Ryzen 7 1700 3.0GHz (Turbo up to 3.7GHz)
Processor Core: 8-Core
Memory: 16GB DDR4-2400
Max Memory: 16GB
Memory Slots: 2
Graphics: AMD Radeon RX 550 4GB GDDR5
(Dual Link DVI-D + HDMI + DisplayPort)
Hard Drive: 1TB SATA 7200RPM
Optical Drive: Ultra Slim SuperMulti DVD±RW drive
Audio: Integrated 5.1 audio
Network: 10/100/1000 Gigabit Ethernet
Wireless: 802.11 a/b/g/n/ac
RE: multiple cores. While many tasks in Photoshop are not fully multi-threaded, there still are certain effects that are. Here is a link to different benchmarks: Adobe Photoshop CC Multi-core performance. If you'll be doing any video editing, then multi-threading is fully utilized. Programs like Adobe Premiere will also use your graphics card to speed up rendering even more. Also, Turbo Boost is something that's decided by the OS and computer BIOS: not an application. If the OS requests higher acceleration, then Turbo Boost will be enabled. On laptops, where the computer is optimized for power savings, there can be brand settings for throttling Turbo down (and it will also be throttled down if the system detects any overheating).
One potential bottleneck I see with the specs is the HD. While ordering the computer, I would buy a solid state drive (PCIe M.2 is the fastest form factor now). There is software for mirroring the installed OS and software from the packaged 1TB drive and then you can set the SSD as your primary drive. You can also add larger platter drives for storing data. I'm surprised that the max memory is 16GB, but it should be fine as a photo workstation.