The Enlarge spell does not state one way or the other whether it changes a creature's size category. That certainly does leave a certain amount of room open to interpretation.
On the one hand, it is reasonable to believe that a character over six feet tall whose since is increased by 50% becomes large, since there are large creatures suchs as ogres that the MM describes as only being nine feet tall (which contradicts dcollins' remarks that a size category constitutes a doubling of height from the previous category).
On the other hand, it is also reasonable to believe that a 1st-level spell should not convey the considerable benefits of a size increase.
I wrote the sage on this one and never got an answer. I'm suprised it never made its way into the FAQ.