It also nicely captures the tendency to resolve the average duels with bokken, which emerged in later period. It followed the use of the bokken as a training weapon, which essentially furthered swordmanship in Japan in general. If not because making mistakes became more of a learning experience than a flirt with the reaper, than at least because it meant fewer students (and even sensei) got bits and pieces chopped of that were quite neccessary for holding a sword and fighting with it.
OT: I have some experience with escrima and it is generally good fun. At times it has the playful feeling you see at capoeira, but there's less acrobatics, and people generally hit you with sticks (or daggers / swords, but nobody sane spars with real weapons I guess). If you're looking for a more rounded art I suggest you either try kobudo (okinawan weapons generally), Katori shinto ryu also teaches weapon techniques and it is a highly respected tradional art (to the point it was recognized by the Japanese governement as cultural heritage or some such thing).
Obviously, genbukan would be a good option too (bujinkan or jinenkan too obviously. I can't speak for Bujinkan or jinenkan, but I in genbukan it will take quite some time before you are eligeble to properly grade in bikenjutsu or any other weaponart for that matter. However, since you will have devoted a lot of time on taijutsu by than, you are quite likely to become a better martial artist, be it with or without a weapon, you always need to incorperate proper taijutsu. A sword does not mean you can no longer kick, lock, evade or escape.
In escrima you learn these things once you get a bit more familiar with your sticks, using weapons to lock and hold and such things. But, if you want to know more about escrima, indeed the best thing to do (as for any other art) is go see for yourself and try it out.
oh, one other thing. You say you are looking for a weapons art involving immediate sparring with a weapon. A word of caution is in order though. You may think you will excell at once, but truth of it is that before you get any good at sparring in any art, you usually will have suffered quite a few good beatings yourself. The problem with contactfighting with weapons is that it can be dangerous, unless proper protective wear is chosen. Which brings me to the third option you have, although it is a bit harder to find i suppose: Historic European Fighting arts. Medieval European swordfighting is actually more and more emerging as a martial art on its own, even though it is still more or less in its infancy. If you find a good training hall it can be very fulfilling though. And i get the impression from your post that this might be exactly what you are looking for. Many people still think martial arts should be asian. Strange, perhaps, considering the fact that the west has its own rich and long history of instruction in the fighting arts. Anyway, this forum has a special secion for medieaval arts, i suggest you check it out.
whatever you choose to do, I wish you a stout heart and a resolute mind. Good luck.