The simple answer is yes, the sword work we do in aikido is descended from one or more of the sword styles studied by the samurai.
Aikido sword work (often referred to as aiki-ken) is not a complete system or style. Rather, it's a subset of sword techniques and kata that relate very closely to our empty-hand work.
Meik Skoss states in the article (linked below) that "... the weapons training sequences most often associated with Ueshiba-style aikido most clearly resembled those of the Kashima Shinto-ryu."
Ueshiba is, of course, Morihei Ueshiba -- the founder of aikido.
I hope this helps!