That's beyond the current functionality, and probably extremely difficult to implement (though they managed to figure out how to do line styles, so there's hope). You should file a feature request at Adobe - Feature Request/Bug Report Form and include a clear explanation of how adding the feature will help users.
My workaround has been to build a 2 column/2 row table (messy but manageable & adjustable):
Put the "W' in the first column, 2 lines of type in the next column adjust the row height.
Merge the next row, add remainder of text
Not a perfect solution, but I have used the vertical justification in conjunction with a baseline grid. The result is below (sorry for the larger image). When this combination is possible, the result is visually "close enough" for me.
You can see that the sentance highlighted by the red line has moved up in the right-hand screen shot. Even so, the visual spacing at the drop cap is pretty well maintained.
Take care, Mike
I use drop caps and vertical justification all the time and have never run into problems. What do you have your first baseline offset in the text frame options set to? Try setting it to leading.
Another workaround would be to anchor a text frame for the drop cap character(s) and manually adjust the frame (and characters within) visually to what ever the amount of vertical space your two lines take up when justified. Since the space between lines will be different when the number of lines-per-page is different, the size of the drop cap character can't be uniform across pages, so you have to decide if that's OK or not. And if you go back to edit a page with a drop cap in a way that changes the line count, you will have to adjust the drop-cap size again (manually). It's more work, and a bit riskier if you're used to automatic drop caps, but it won't look like your example.