Would the size of an integer depend upon the compiler, OS and processor?
The answer to this question depends on how far from practical considerations we are willing to get.
Ultimately, in theory, everything in C and C++ depends on the compiler and only on the compiler. Hardware/OS is of no importance at all. The compiler is free to implement a hardware abstraction layer of any thickness and emulate absolutely anything. There's nothing to prevent a C or C++ implementation from implementing the
int type of any size and with any representation, as long as it is large enough to meet the minimum requirements specified in the language standard. Practical examples of such level of abstraction are readily available, e.g. programming languages based on "virtual machine" platform, like Java.
Howerver, C and C++ are intended to be highly efficient languages. In order to achieve maximum efficiency a C or C++ implementation has to take into account certain considerations derived from the underlying hardware. For that reason it makes a lot of sense to make sure that each basic type is based on some representation directly (or almost directly) supported by the hardware. In that sense, the size of basic types do depend on the hardware.
In other words, a specific C or C++ implementation for a 64-bit hardware/OS platform is absolutely free to implement
int as a 71-bit 1's-complement signed integral type that occupies 128 bits of memory, using the other 57 bits as padding bits that are always required to store the birthdate of the compiler author's girlfriend. This implementation will even have certain practical value: it can be used to perform run-time tests of the portability of C/C++ programs. But that's where the practical usefulness of that implementation would end. Don't expect to see something like that in a "normal" C/C++ compiler.