Would the size of an integer depend upon the compiler, OS and processor?
The simple and correct answer is that it depends on the compiler. It doesn't mean architecture is irrelevant but the compiler deals with that, not your application. You could say more accurately it depends on the (target) architecture of the compiler for example if its 32 bits or 64 bits.
Consider you have windows application that creates a file where it writes an int plus other things and reads it back. What happens if you run this on both 32 bits and 64 bits windows? What happens if you copy the file created on 32 bits system and open it in 64 bits system?
You might think the size of int will be different in each file but no they will be the same and this is the crux of the question. You pick the settings in compiler to target for 32 bits or 64 bits architecture and that dictates everything.