Your hard drive will have a SATA connection, so yes you can just unplug it, and plug it into your PC, when it's turned off, then the PC should find the disk, and load the drivers, upon booting.
You can then run any software loaded on your PC, to check it, from the basic Windows options, to thge most expensive software, and numerous free utilitiies.
First try your Windows options, open up the Computer option, from the start menu, or shortcut, you might have on your PC, right click, on the drive, select properties, and tools, error checking.
If this fails try a free utility, a quick internet search found this:
Code:
https://www.lifewire.com/free-hard-drive-testing-programs-2626183
But there are many other options, just do an internet search for free hard drive software, or best error checking software for hard drives, etc...