In theory synthetic crosses, which consist of two major legs may move while cross rate remains the same. For example: currency A rate to USD is 2 and currency B rate is 1. Cross rate of A/B is 2. Rates change so that currency A is 4 and currency B is 2. Obviously if you were long A/USD and short B/USD you would profit while cross rate still remains 2 so if you were long cross you would gain nothing. Now the question is: does it happen in reality with major crosses, such as AUDCAD etc? Guess they're heavily arbed out with major pairs?
Of course they're heavily arbed. Basically on such liquid market the inefficiencies your talking about are extremely rare you have to catch the moment. Basically some powerful movements can produce that but they are short-lived and unstable.