The following code fails:

import pickle
import numpy as np
import quantities as pq

pickle.loads(pickle.dumps(np.array(1,'O')*pq.V))

Inside Quantity.__setstate__, the call to np.ndarray.__setstate__ fails with TypeError: object pickle not returning list. So far I do not understand more about this.
Of course, there is rarely a good reason to have dtype=object with quantities, but if the constructor accepts it, then pickling should work too.