RE: display printed pick ticket status as a column in a saved search
I don’t believe there is a way to tell if a Item Fulfilment has been printed (picking ticket) already.
Is this what you were after? Or were you instead asking about having your Sales Order search show you whether an Item Fulfilment has been generated for it (and its status)?
If the latter, then yes, it is possible (you can either use the “Fulfilling/Receiving Transaction : Status” join/field)