No. Logic is nothing more or less than a tool to arrive at truth. Actions can be driven by logic (in the sense that if I want a certain outcome, I can reason logically about what actions I should take to achieve it), but emotions can't. If an "emotional" person is a person who feels a lot of emotions, and a "logical" person is a person who uses logic to arrive at conclusions, then it is possible to be an emotional person, a logical person, both, or neither. A person who is just emotional might see a news story about a politician who kicked a puppy in San Francisco at 8 a.m. PST and then flew to Philadelphia to steal candy from a baby at 11 a.m. EST on the same day, and be angry at the politician. A person who is just logical might read the same story and realize that the story must be incorrect, because the way time zones work means that the politician would have had to have been in two places at once, but feel nothing. A person who is logical and emotional might read the story and realize that it must be incorrect, and be angry at the newspaper for lying or making a mistake, and uneasy until he or she knows for sure whether the politician kicked a puppy and stole candy from a baby. A person who is neither logical nor emotional might read the story, not realize that it is false, and not feel anything about the fact that the politician kicked a puppy and stole from a baby.
In other words, logic and emotion are not opposites, and they're not mutually exclusive.