Just to be clear -- construction data is
not a map update. It lists areas under construction, so you can drive around delays. You should not expect construction data to supply new map information, e.g. a new housing development or whatever. Map data is only updated with new versions of S&T.
The New Yorker did a fairly informative article on Navteq in 2006, around the time they got bought by Garmin. Here it is:
http://www.newyorker.com/archive/200.../060424fa_fact
Average time for Navteq to close out my error reports is about 3 months, but then, I don't live in a big city so you may see better speed. They release data quarterly, so there could be an additional 3 months before it shows up on online mapping sites. Then, up to 9 months before it makes it into S&T, depending on whether it makes the cutoff for the next version.
Presumably, the "Send Map feedback" menu item under "Tools" will look up the appropriate data provider and pass along the feedback. In most areas in the US, this will be Navteq, so you might as well report it directly.
P.S. I think "Send Map feedback" is a terrible euphemism. People won't think to click on it. "Report map error" is more direct, assuming people ever think about finding it under the Tools menu. If you search for "error" in Help, the first result is right, but the title is similarly euphemistic: "About the feedback wizard."