I'm not sure which version of Quark 4 you are using; mine, version 4.11, will (technically) allow a none-backgound.
HOWEVER that means that only a pure white will drop out, and a jagged grey margin appears around objects if they have any non-white border at all (as most do).
Two solutions I've used:
1) send the image to the back, with a white background (and put things that "show through" the background on top) and
2) use a clipping path from Photoshop to isolate the object.
Hope this helps