Yes, I think a female should be allowed to ascend the Imperial throne of Japan.
As has been noted, by others (Index, Silverbackman, Hiroshi66, 名無し), there is precedent for the ascension of an Empress to the Imperial throne. I would offer a couple more thoughts about such precedent . . .
If we extend the argument even further back to mythic lore, one might also consider the relevance of the creation myths which features the
goddess Amaterasu Ōmikami as the progenitor of the Yamato line which in turn leads to the Japanese people and the Imperial line. I am not confusing myth with historical precedent here, but only note these stories because I believe in a culture's mythos important values can be discerned. In this case, I believe that legends and myths surrounding Amaterasu demonstrate that there is long-standing potential within the Japanese culture for acceptance of female ascendancy into power.
Also, consider that prior to the 12th century, women were still able to be effective landholders in Japan, only being greatly reduced in cultural status, privilege, and position with the rise of the
bushi and the Kamakura shogunate which shifted the reins of land-ownership to the military bureaucracy (though a general decline in the status of women in Japan had been in effect for a couple of centuries by this point). Again, this is just to say that there are times in Japanese culture/history when women were afforded certain measures of power.
Beyond a cultural support (at least in the broad context) for the ascension of a women to the Imperial throne, one might consider the nature of the throne itself and whether or not it is suited to an Empress.
First, since 1945 the Imperial throne has been greatly reduced in its political clout. I would argue that due to international agreement and constitutional restraint, the Emperor of Japan is no longer a political head-of-state, but rather a 'cultural' head-of-state.
As noted in a National Geographic article, ""One of the major roles of the imperial family is to preserve traditions like [cormorant fishing]," said Ryuji Takahashi, manager of the Special Ceremonies Department of the Imperial Household Agency, the government unit that runs the palace and pays a small group of fishermen like Mr. Sugiyama. "It's not very economical, but it is an important part of our
cultural history," he said." (National Geographic, Januray 2001, p.100)
So, I interpret the role of the Imperial throne to be that of symbolism; that is, the Emperor/Empress represent the traditions, the pageantry, the grace, the nobility, the heritage, and the grandeur of what is finest in Japanese culture both past and present. This is a function that I don't see as necessarily being sex specific. In fact, by allowing a Empress to ascend the throne, I think Japan would be making a fine statement about the continued progress of its culture.
As to whether or not there should be such things as emperors and empresses in the first place . . . well, I believe that hierarchies are an inherent trait of human nature; some people will be high and some shall be low in the scheme of things. I can't even really think of it as a right or wrong issue, but merely as something that just is. That being the case, I figure perhaps the best way to approach the concept of sovereign individuals/institutions is to try and ensure than you have the best sovereigns/institutions as possible. Considering the nature of the Japanese Emperor, say, about 65 years ago compared with now . . . I think the Imperial household is doing a mighty fine job these days.
Finally, considering that some revisions to existing law would need to be made to allow for a modern day empress . . . hey, where there's a will there's a way, ne?