My answer is "yes" as anyone with IV and eczema in my family also has asthma. The eczema abated with adulthood while the asthma (aggravated by allergies ie.pollen) persisted through adulthood.

I however have moderate IV but have no history of either asthma or eczema. So the correlation is not absolute.

Based on what I've read, my layperson's understanding of the genetics is that the connection is between the filiggrin gene responsible for ich vulgaris and a predisposition for eczema/asthma.

Here's a news article on the gene discovery made in 2006.