Never underestimate flattery ...regardless of one's intellect...
IMO, Dubya and his handlers are obviously hoping to pluck more than a few Catholics who would otherwise be fence-sitting until election.
I would agree with you about this situation's looking mighty suspicious if the President had chosen this occasion to first show up on the papal doorstep. However, GWB and the Pope have an established relationship.
For one thing, President Bush consulted with Pope John Paul, in addition to other moral leaders, when he was considering fetal tissue research. He recognized the Pope as a moral authority, and respected him greatly as being a man of faith. The President ended up choosing a middle road, rather than the one recommended to him by the Pope, but by his seeking spiritual guidance, GWB showed he was really making an effort to come to the best moral decision. This was not for votes.
The President and the Pope have a relationship, and from what I've gathered about these two men, there are both spiritual and temporal ties that bind them. Maybe GWB wants to honor John Paul now, while he's still President - just in case the election doesn't go his way. We don't know for sure, because we're not two flies on the wall, so it's a possibility.
Ronald Reagan also had ties with John Paul. Both Reagan and Bush responded to the inner mandate of defeating evil.