Gotta bark with the dog on this one.
While the sheaves (and could we please eliminate the word pulley from this site) may be of sufficient diameter the issue is the width of the sheave. Regardless, we know that as we reave the line the point at which it is going to be toughest is as the line passes over the sheave. That's where we're going to give it that little extra tug. Then three things can happen, two of which are bad. First: the sheave is of appropriate size and the line goes over and works just fine. Second: the sheave is of inappropriate size, the line goes over, and proceeds to either foul or abrade severely as we employ it in sailing. That could be dangerous if discovered while trying to lower the sail in an emergency-or could make an emergency out of a routine operation. Third: The new line fouls at the truck and we have to climb the mast anyway.
All in all, the dog's suggestion really has no down side. Running all line without knowing what is actually at the truck in the way of a sheave is sort of like landing a shark in a boat. If you're not sure that he is real dead, you might want to consider a Plan B before he's actually in the boat.