No. As I'd noted, when Suggest was a Lab project the Google Suggest numbers originally correlated roughly with the the number of pages returned that contained suggested target phrases, not with search popularity.
Google's help page indicates that if you were looking at personalized results, Google would also be factoring in search popularity. But, if you're not signed in, "no history-based suggestions are displayed." This latter phrase, "no history-based suggestions", of course, might be intentionally ambiguous in terms of how search history enters into the Google algorithm as a whole.
As it turns out, Google is the only engine that returns subdirectory suggestions for microsoft.com. I see Google suggesting a very occasional subdirectory for other domain searches, but they're not nearly as frequent as they are on Microsoft. So these may be very special cases... perhaps worth exploring.
It's very difficult, though, to get straightforward search results (on any of the engines, not just on Google) for searches including the slash character, so this subdirectory co-occurrence is not easily described by simply saying that if the terms co-occur enough on a page, Google will include them in Suggest. Nor does treating the slash characters as delimitors give a clear picture of what Google is looking at.
It may be that Google is coming up with its subdirectory suggestions by looking at a combination of domain.tld co-occurrence with both the keywords in the urls and in occurrences of the full subdirectory urls on the pages. (Microsoft urls often appear in full on referring web pages). Google might also be using weighting factors analogous to those they use in choosing Sitelinks.
Google is also using phrase-based indexing at this point, not just word matches, and this further complicates simple considerations of number of pages returned for associations with your brand name.
But, bottom line... you've got to do a lot of online "promotion" to get your brandname associated on other websites with terms other than the word "sucks".