Can the average case of an algorithm be $ O (n logn) $ if the optimal running time of an algorithm is $ Theta (n log n) $?

Suppose the best time to run an algorithm is $ Theta (n log n) $. Can the average execution time of the algorithm be $ O (n logn) $? Since $ O (nlogn) $ would imply value even going underneath $ n log n $ would therefore be inferior to the best linked case of $ Theta (n log n) $. Is it possible?