With AutoCAD built-in command Array/ArrayXXX, (take ArrayRect for instance) the result entity array can be "Associated", or "Not Associated". The former appear as a single entity grouping all entities together, with special grips, which allow user to change the array (row/column/distance...). Actually, the array is a dynamic block reference. The latter is simply multiple individual entities places in row/column/distance. Also, the former can be exploded into individual entities.
I am not sure why you ask if there is ActiveX (COM API) to do it in this .NET API forum, but anyway, with COM API, the answer is yes or no. Yes, AcadEntity has method ArrayPolar()/ArrayRectangular(). But no, they do not result in associated array. The array generated is an array of non-associated individual entities.
With either .NET API or COM API, one can easily programmatically generate an array of non-associated entities with minimum math. But to get an array of associated entities as AutoCAD built-in command does, there is no API exposed, I think. As alternative option, we can group the array of individual entities together, which can also be done easily with .NET API/COM API.
To mimic AutoCAD built-in associated array (with special grips) programmatically, it might be doable with either Overrule, or Associate Framework, or the combination of both. In this case, the attempt would only be possible with .NET API (or ObjectARX C++), but not COM API. As aborementioned, the associated array is a dynamic block reference, and there is no API available to programmatically compose a dynamic block, we can only try to mimic the AutoCAD built-in one as close as we can, until one day Autodesk makes dynamic block composing API available, if it ever happens.