What Frederik said is very good. The most successful imitations of modern instrument are on early 20th century orchestral organs. These organs are a radical departure from standard organ design, and while they can play transcriptions of orchestral works, and certain kinds of pieces meant for such instruments, they do less well at blending many stops together into a full and rich chorus. . .or at least they do not produce the traditional kind of organ chorus, and therefore it is difficult to use them to play most organ repertoire. But they can be beautiful sounding instruments. One of the best in the US is a Woolsey Hall at Yale University.
Keep in mind that in most pipe organs built according to traditional tonal concepts, the imitative sounds are more or less imitative, and often less, because they are designed for specific tonal functions in terms of blending with other stops. For instance, an organ trumpet may sound different from a real trumpet, but it works very well for its intended use in organ music.
But I suspect that the sounds you're seeking are nearly impossible to recreate on the organ. While it is possible to get fairly close in overall tone quality, the swelling and receding effects are produced with great effort through Swell shades, as Frederik mentioned, and producing this effect on each note like a real clarinetist would be extremely difficult if not impossible.