Yes and no! <S> Sorry for the ambiguity! I think it depends on the plant's health, if it bloomed early enough in the warm season, and if the plant had enough days to grow a spike before the cool season arrives. The only reason I say this is, that I own a Nishidemiyako 西出都 West Side of Kyoto plant, it was in bloom when I got it at the end of July 2013, it started developing a spike in September and it is in bloom now. It has been in bloom for the last three weeks. So the answer is "yes".
I own other Neofinetia that were in bloom early June timeframe, and those plants have not re-bloomed this year. So the answer is "no".
More ambiguity, another person may own the same plants I refer to and may achieve better results. I guess when it comes to Neofinetia, YMMV applies.