Thinking about that scene in Game of Thrones where Bronn fought a knight, and he won because he was more agile whereas the knight was not. Seems like in this situation armor would be a handicap, not a benefit.
The short answer is "yes" and "sometimes".
Depending on exactly how one defines "duel" - typically, organised regulated combat between two private individuals - there are types of fights that might or might not be called "duels", such as pas d'armes with sharp weapons, which occupy somewhat of a middle ground between duels and tournaments. Other types of fights are clearly duels. Notably, they were often a feature of the legal system: judicial duels intended to determine the guilt of the accused, or to resolve a dispute between two parties. We have information about judicial duels from various law codes and records of cases.
The rules often specified what armour and weapons were to be used; these were, if specified, usually the same for both fighters. Sometimes the weapons and armour were not specified, but the rules were that both had to be equally equipped.
Some examples:
In Norway and Iceland, a formal duel called hólmgang developed (literally, "going to the island" - the duels were often fought on islands). Rules (which varied over time) are recorded in a number of Icelandic sagas (Kormáks saga, Svarfdælasaga, Egils saga Skallagrímssonar, and others). The most famous description of a hólmgang is from Kormáks saga: "Bersi struck the first blow, and cleft Cormac's shield; Cormac struck at Bersi to the like peril. Each of them cut up and spoilt three shields of the other's. Then it was Cormac's turn. He struck at Bersi, who parried with Whitting. Skofnung cut the point off Whitting in front of the ridge. The sword-point flew upon Cormac's hand, and he was wounded in the thumb. The joint was cleft, and blood dropped upon the hide. Thereupon folk went between them and stayed the fight." Hólmgang was banned in Norway in 1014. For much more detail on hólmgang, see http://www.vikinganswerlady.com/holmgang.shtml
From the Sachsenspiegel, a German law code written c. 1220, this illustration shows two fighters in a judicial duel. Their dress and weapons are regulated: the only armour allowed is the shields, and neither is allowed an (initial) advantage from the position of the sun.
The Chronicon of Thietmar of Merseburg describes (briefly) a judicial duel in 979 between Gero, Count of Alsleben, the accused, and Waldo, his accuser. The duel was fought on an island (cf hólmgang). Gero wounded Waldo twice in the neck, but Waldo then struck Gero in the head, and Gero, unable to continue, conceded defeat. Shortly afterwards, Waldo died of his wounds. Having been found guilty, Gero was executed. The chronicle doesn't describe the armour and weapons used. (pp 133-134 in Warner, David A., Ottonian Germany: The Chronicon of Thietmar of Merseburg, Manchester University Press, Manchester, 2001)
An armoured judicial duel is shown in a sequence of illustrations in the Königsegg Talhoffer manuscript: folios 9v to 24r in http://wiktenauer.com/wiki/Talhoffer_Fechtbuch_(MS_XIX.17-3) Note that both fighters are fully armoured, and the fight finishes with wrestling with daggers. Preparation for such duels appears to have been an important purpose of the armoured fighting sections of late Medieval German fightbooks.
A judicial duel between a man and a woman, the man armed with a club and standing in a hole in the ground, and the woman armed with a "rock in a sock" is illustrated in another Talhoffer manuscript: http://wiktenauer.com/wiki/Hans_Talhoffer/W%C3%BCrttemberg
Post-Medieval, in 1547, the judicial duel between Jarnac and Châtaigneraye. Both fighters were equally equipped, with armour. Jarnac won by incapacitating his opponent with hits to the exposed backs of his legs (such a blow becoming know as le Coup de Jarnac as a result). A detailed description and analysis is available at http://www.thearma.org/essays/DOTC.htm
Thinking about that scene in Game of Thrones where Bronn fought a knight, and he won because he was more agile whereas the knight was not. Seems like in this situation armor would be a handicap, not a benefit.
The fight choreography in Game of Thrones is often very unrealistic, and should not be considered a reliable source for how real fights (duels or otherwise) would proceed. Typically, in a duel, one side having full armour and the other not would be an enormous advantage to the party with armour.
