Note that I'm not trying to actually do this (it was just a simple example, but somewhat equivalent in fucntion to actual use cases), but I guess that if we can implement a NAND then the rest would be possible too (in some awkward way). One recent example of an actual use case is this:
(I'm of course not thinking of representing eg scalar floating point values at the type level, in case the bit-operation-example seems to suggest something like that 
but rather I'd like to be able to "compute" the types (for the mutlivectors), and only the ones actually needed for a given program, at compile time rather than runtime, to make it an acceptably efficient GA implementation, without code generation, ie replace code generation with generics (expand quoted post for details). But this is getting off topic).
I do think the (still unanswered) question of this thread is clear in the OP and the title.