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In my personal experience NO Staffie's do not drool after long walks over the years i have owned 6 staffies and none of them drooled.
An American Staffordshire Terrier may be right for you. If you don't want to deal with... Legal liabilities (public perception, future breed bans, insurance problems, increased chance of lawsuits) An extremely careful search to be sure you're acquiring a stable-tempered individual.