By conducting a basic test by running a simple C++ program on a normal desktop PC it seems plausible to suppose that sizes of pointers of any type (including pointers to fun
No, it is not reasonable to assume. Making this assumption can cause bugs.
The sizes of pointers (and of integer types) in C or C++ are ultimately determined by the C or C++ implementation. Normal C or C++ implementations are heavily influenced by the architectures and the operating systems they target, but they may choose the sizes of their types for reasons other than execution speed, such as goals of supporting smaller memory use, supporting code that was not written to be fully portable to any type sizes, or supporting easier use of big integers.
I have seen a compiler targeted for a 64-bit system but providing 32-bit pointers, for the purpose of building programs with smaller memory use. (It had been observed that the sizes of pointers were a considerable factor in memory consumption, due to the use of many structures with many connections and references using pointers.) Source code written with the assumption that the pointer size equalled the 64-bit register size would break.