Technically no as Apple’s OS installer won’t install the OS on your system.
Frankly, I don’t recommend running High Sierra or newer on these older SATA based systems as APFS has issues running on SATA drives. APFS is a very chatty I/O and SATA drives don’t have the deep I/O buffers the PCIe/NVMe drives have (blade SSDs)
There’s nothing wrong using Sierra! So far most Apps don’t require High Sierra or newer. The the few that do are heavy I/O apps that are used to process music, photos and videos. This is where the amount of RAM and video services of the system become more important.
OK, still want to run it, I would very strongly recommend you first make a bootable external drive and then copy over your stuff over using Migration Assistant that way you have a bootable backup drive. Put this drive some where safe. Then go to here [https://www.reddit.com/r/BigSurPatcher/|BigSurPatcher]. I’ll warn you! You might brick your system! Apple is already encountering issues with the Mid 2013 systems being bricked! [post|666066] I would wait and I would recommend you only play around on a test system with 16 GB or RAM and plenty of drive space.