"They say no"......
http://www.ipm.iastate.edu/ipm/hortnews/1996/8-23-1996/crosspol.html
Since they have a similar flowering habit, bloom about the same time, and are members of the same plant family, it is logical that gardeners might assume that squash, melons, and cucumbers will cross-pollinate. Fortunately, however, this is not true. The female flowers of each crop can be fertilized only by pollen from male flowers of the same species. Cross pollination, however, can occur between varieties within a species. Cross pollination can be seen in the squashes and pumpkins. Summer squash, pumpkins, gourds, and some types of winter squash belong to the same plant species Cucurbita pepo. All species members may cross with one another. Thus, an acorn squash will cross pollinate with a zucchini or a miniature gourd. However, muskmelon (
Cucumis melo) and cucumbers (
Cucumis sativus) belong to different species and will not cross with each other or members of the
Cucurbita genus. An example of incompatibility can also be seen in the animal kingdom. Cardinals cannot mate with blue jays. (The part of the lesson about the "birds").