Unfortunately simple POST to BIOS is meaningless except to find if CPU is totally slagged. Unless its "throw away with no pain" cheap I'd try to get some sort of sustained stress testing (free software) first even if its just 15-30 minutes standing in buyer's house. Usually error rates increase as the CPU get hotter under sustained stress under conditions close to maximum performance. Many CPUs can go minutes or hours if not stressed before having error. Even then many errors can hide under hardware or OS recovery especially if you don't read event logs or have them send warnings to desktop. Thus stress test software exists to heat CPU and log all errors directly.
Regardless it can be almost mandatory to stress test your hardware builds built including other peoples used parts. Do this BEFORE investing too much time on software installation or placing the machine into production. You can lose lots of time or data to bad parts when rushing software install, configuration or usage. But simply monitoring a 24-48 hour stress test can find a hardware issue before you even add an OS.
Cheaper Used CPUs can be great for specific purposes where risk is acceptable.
Example: first low-end throw-away CPU in a new build while you wait for top dream CPU to fall to reasonable price (or your savings to increase). This allows you to have OS etc. ready before final CPU (and maybe final memory expansion/video card). Once proven these parts can even become your hardware test parts for that rig after you upgrade CPU etc. ... should you have later hardware problems with your build. If its been a long time since you build last computer for whomever then even the low end CPU might be faster than their old rig.
Many home network server/appliances do not require a lot of cutting edge power. Again stress test new hardware builds (CPU, memory, storage system) incorporating used parts of unknown providence to avoid unnecessary outages, reinstalls, and data loss or corruption.