There appears to be a connection:
People who scored high in attachment anxiety (for example, they agreed with statements like “I worry about being abandoned” and “My desire to be very close sometimes scares people away”) tended to be better at spotting lies and made-up stories….
To see if the lie-detection skills associated with anxious attachment have any benefit in real life, Ein-Dor and Perry recruited 35 semi-professional poker players, assessed their attachment style and then observed their performance in a local poker tournament. Each participant was allocated at random to join in with a group of seven other players at the event. As they predicted, the researchers found that the participants who scored higher in anxious attachment tended to win more money in the tournament (on average, a one-point higher score in anxious attachment was associated with winning an extra 448 chips).
The Dish 