I haven't seen any data that lines up with your idea - although it does sound like a possibility. Some of what I have seen showed a slight decrease in the average length of a search phrase on Google for Q4 of 2009 - although not by very much.
One possibility for the slight downward trend is the rise of mobile use, which makes more typing less likely. Another possible explanation is a flaw in the study methodology. There would be many pitfalls, for example how does any study score full URLs that are typed or pasted into the search box? Each dot, forward slash or colon could be counted as a word separator.
Up until Q4 the length seemed to be growing a little bit every quarter, and most recent data studies show an average search term of just below three words.
As I think about it, that average of right around 3 words means a lot of search phrases that are 4, 5 and 6 words long, and Google Search Suggestions might work against those much longer searches, too, even as they increase the 2 and 3 word length.