Yes, this is the case, e.g. in micro controllers, where the program is stored in EEPROM. You can store data in program memory (e.g. constant strings) but you need to access it in a special manner.

> Has there ever been an architecture where data pointers could have a different representations?

At least conceptually, this was the case in early GPUs, where there were different memories for different access patterns. Memory area for constants, another one for global read only memory, and a third area for thread-specific read-write -memory and a fourth that was shared between groups of threads.

Whether they were actually different physical memories and whether they had different address spaces is another issue (they at least partially did, some stuff was on chip, some was external DRAM), but this was how it was conceptually seen by the programmer and the way early GPGPU APIs worked (early versions of CUDA and OpenCL).