not really, every one says he did, but in reality all Edward did was tell Harold to take care of his wife and Kingdom, given that Harold was more or less the PM of the time, the king could of meant "be Regent" or anything else, people wanted Harold has king so they took it to mean what they wanted.
I've got to be honest, I can't think of a anything like contemporary account nor any modern historian writing on the subject who has suggested that what Edward really meant was for him to be a regent.
I also have to be honest and say that given that Edgar was chosen as King by the people of London and the northern Earls after Harold's death (when the situation was much more serious), I think that if there was any possibility Edward meant Harold to be regent for his Kingship, Edgar would have been made king on Edward's death.
You need to bear in mind that the northern Earls were not wholly Harold's friends, it took a lot of politicing to make sure they would not object to his becoming king. Earls Edwin and Morkere/Morcar had a family history of fueding with the Godwins, there was some sort of horse trading clearly following the crisis of the northern revolt Tostig to get them on Harold's side (including Harold marrying their sister) and even in 1066 there are indications that Harold didn't wholly trust them. I suspect if there had been any doubt over what Edward had really meant on his deathbed they would have used it to halt Harold's election as king.
But I suspect we'll have to agree to disagree on this one