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The _int_ type is assumed to be 4-bytes wide: https://github.com/opencv/opencv/blob/master/modules/core/include/opencv2/core/hal/interface.h

I think there is no explicit check anywhere, but implicit assumption can be found in many places:

bit shifts and masks; not sure if this function will work with 64-bit int, but it will definitely broke for 16-bit.
we have generic 128-bit SIMD C++ implementation which assumes 128-bit register = 4 x int values
some algorithms use SoftFloat library with assumption int = int32_t (example)
...
the type identifier for int matrices is named CV_32S