First, I think there needs to be a distinct difference made between praying/invoking saints and asking saints to pray for you, which seems to be the main point of this thread.
It is important that the saints are not looked at as necessary or our "way to God", the largest concern that Luther had regarding them is the idea that saints are meritous and overflow so much with righteousness from their lives that they can in some way "help" us either physically or spiritually. This is explicity prohibited in scripture and counter to the reality of righteousness by faith alone. So we do not look to them for aid or pray to them as we would God. We do not see them as mediators because Christ is our mediator and we are all a "priestly nation".
As for asking saints to pray for you, is that any different than asking members of your church to? In truth, you are asking saints to pray for you when you do that. As to saying there is a distinction between dead and alive in body I must disagree. For we die in the flesh in baptism and likewise rise with Christ in that baptism. Do we not commune with these people at the Lord's Supper each Sunday? Are we not part of one body? When we say in the great thanksgiving that we join ALL the hosts of heaven as we sing the sanctus, do we lie, is there not a bond or communication. Luther spoke of the brotherhood of the saints as a common treasury that shares in prayer, sin, etc. We are inevidably bound to the saints past and present. This includes the "famous saints" if I may, but also the whole body of believers. Our faith, scripture, and creed remind us that this bond goes beyond the boundries of death because we all died at baptism. We are all one body, and the hand can never be far from the arm.
Is it any good? Is it any more effective? I would say it is not "necessary". I would also say that one could not argue it to be more or less effective than when any "living" saint prays for you.
So this gets to the point should we ask them? I would say no. First it is unnecessary in as much as prayer to Christ is the way to the father. If they were to pray for you, that is the mode in which it would happen. Second, it can lead to misunderstandings and even idolotry or an obsession with them over living saints or worse yet turn their attention from Christ. Third, I would argue that they are praying for you already. Paul calls us to "pray without ceasing" and I see no reason that this would end in death. If we believe in the communion of saints we should believe that they are present with our prayers and pray with us every time we gather. The common treasure idea of Luther's suggests they share in our prayers and sufferings and we in their before. Christ causes a paradox of this union of past with present. Just as Christians around the world pray for one another and all humanity without our knowing or hearing, I see no evidence that those who have passed to paradise before us are not doing the same. But in the end we know that our trust, faith, and purpose should rest wholefully in Jesus Christ. And whether or not saints living or dead pray for us we need not concern ourselves with knowing entirely, for Christ hears prayer, and the healing of the nations will flow from him.
Peace be with you