The chest is 68" tall so I assume it would be visible
Tim,
You are, what, 6' 3"? 6' 4"? From the vantage point of an 18th century man, the top would probably not be seen.
Do you know if the sides are frame and panel? Or is the case dovetailed? There are probably a number of ways that this could be built so that the top is flush with the top of the molding.