Yes but why would you? Radioactivity means you can't reoccupy the land yourself.
If dispensing misery is the goal, we have more effective chemical and biological weapons which are less militarily useful for the same reasons as a high-fallout nuclear bomb would be.
In a mutually assured destruction scenario, I don't think you could plausibly expect to invade the other country. The world as we know it would be over but some people would survive the exchange, maybe those in power could have a lot of spite and want to completely salt the earth with some cesium nukes to prevent the other country from recovering even after the nuclear winter subsides.
Why would they build the weapon in the first place though? MAD is a deterrence strategy: the weapon isn't meant to be used, but to work you must have sufficient weapons to ensure you get reliable kills on all your military targets.
If this is the plan, then building more weapons than that is a pointless waste of money because you're not planning to use them. If MAD isn't the plan, but rather hostage taking (ala North Korea) then a high fallout device is still useless because you have Assured Destruction if you launch it, but also not enough capability to ensure it arrives (the US can plausibly defend against a "rogue launch").
So again, when would you bother building it? At any given junction you either have enough weapons, or you need more warheads putting heat and overpressure on targets to ensure reliable kills and this deterrence.
Building a bunch of weapons which will cause at most tens of thousands of deaths months later, after you incinerate millions makes absolutely no economic sense and hence why at the height of the Cold War everyone looked at the concept and concluded it wasn't worth pursuing outside of a research analysis.
In a non-MAD employment scenario, you would build them for area denial. e.g. I don't really know how far the fallout would go from some cesium nukes, but maybe if russia wants a moat that lasts a long time but they can't take over ukraine with conventional forces, then they could launch some at ukraine and build their moat that way.
In a MAD scenario, I would view them as a bigger scarier stick to threaten people with.
