A home test won’t. A PCR gives you some idea if you can get them to tell you the CT (cycle threshold) value of your test. The CT value corresponds to how many times the temperature cycled before the amplification signal of the sample became detectable. Lower CT values correspond to higher viral loads.
Definitely. Plus, you can absolutely get different CT values from two different testing platforms. Some PCR tests are more hands-on than others and the result can vary based on the quality of processing and on the settings that are used in the analysis software.