In theory, yes. Intel do this kind of thing all the time, and often their desktop and laptop chips are the exact same die coming off the exact same production line, and then placed into two different boxes, one intended to run at higher clock speeds for desktops, and one designed to run at lower clock speeds for laptops. There are some pretty big issues with taking this route, though. The first is that the low-voltage (laptop) versions of the chips are actually the more valuable ones. They're the chips which have been tested to perform better under tight thermal constraints, so they're worth more than the desktop chips (where you don't care so much about how much power the chip is using or how much heat it's putting off). This means that your handheld, which is going to sell for a lower price than the home console, is effectively going to have the more expensive hardware in it.
The other issue is that even a standard laptop has active cooling, whereas for a handheld console you're looking at a passively cooled chip, which pushes you into ULV (ultra low voltage) territory. Intel does a line of passively cooled chips called Core M, which are used in Apple's MacBook, amongst other ultra-thin laptops. Again these use the same cores as their Core i series laptop and desktop chips, but clocked lower again than the standard laptop chips. One thing you'll notice about the Core M line, though, is that it doesn't go beyond two cores or their more basic integrated graphics. The reason for this is that, at the power and thermal limits Core M has to fit in, you simply wouldn't get much benefit from adding more cores or a more powerful iGPU. A four-core Core M would have to be clocked so low that it would be barely more powerful than the two-core model, and ditto for a version with the better GPU.
What does this have to do with an NX chipset that would be shared between a home console and handheld? Well, Nintendo would effectively end up spending a lot of money on a big expensive die for their handheld, only to have to clock it so low that it would be barely more powerful than a smaller, much cheaper chip. In any case, with separate dies for an NX home console and handheld, Nintendo would be purchasing in the tens of millions of each, which firmly puts them in the higher brackets when it comes to the economies of scale for custom die purchases, so there's not much more for them to gain by merging them together.
