That depends on how Google Prediction's algorithm works. I'm not familiar with it, but in reading the docs it appears they do not consider word association. That is to say, they do not consider which word a sentiment-laden stop word like "not" is particularly modifying.
For example,
"Cake is not close to being as good as french fries!"
"French fries are not cake, but are not bad."
In the above sentences, treating them as a "bag of words" (a sentence model in which word order does not matter) doesn't yield us much insight.
My recommendation is to experiment and let your data results be your guide.
I suspect using stop words will not make much a difference. They should fall below the "noise" threshold of Google's matching algorithm, assuming I'm divining how it works correctly.
You can google-up a list of stop words for several languages. You can also pull many Natural Language Processing libraries. Stemming words might help. Try googling for Porter Stemming or Snowball Stemming" and Java. Lucene/Solr uses this sort of analysis to build up search indexes.
Good luck.