Can I update to the latest version of Android on a generic off-brand tablet?
There's no special procedure that works with unbranded tablets. As the question you've already found describes, if there's no official upgrade from the manufacturer, you need to look for a custom ROM based on a newer Android version. Where can I find stock or custom ROMs for my Android device? gives you some places to look.

There's only one feature peculiar to unbranded tablets and phones. Often, several apparently different unbranded tablets or phones will contain exactly the same hardware, because they're based on the same "reference design". In this case, it may be possible to use a ROM for another unbranded device with the same hardware. It's quite hard for an end-user to know whether this is the case: it's not enough that the tablets are all based on the same SoC, but if all the spec-sheet specs are exactly the same, it might work. Flashing a wrong ROM can have bad side-effects, potentially bricking the device, so I wouldn't recommend trying this carelessly, but it may be that you can find a post on a forum such as XDA developers from someone who has already found a ROM that works on your device.