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In a word, yes it was...although that's not actually the reason for the difference that you quite rightly pointed out in the two specific screen captures that you shared.
The Study-set as seen in the Pilot was actually shot at Fox's Sunset and Western studios (as opposed to the Batcave set which was over on the original Fox lot on Pico Bl in Century City. When the show was green-lit, the show's unit-base and standing sets were transported and reconfigured for the first season at Desilu Culver which would go on to be the show's home-studio for it's run.
That being said, as the show progresses season by season we see further alterations to the study set's phsyical shape. By Season Three, much of the Wayne Manor set (particularly the living room and lobby area) are pretty much gone to make way for the Gotham Public library standing set that subsequently would re-use the physical same space on Stage 15 at Culver. As a result the Study also goes on quite a diet and becomes evident when we look at the framing of any of the study-scenes during the third season, much tighter shots and far less camera movement are used in order try and be as economical with the space available. One of the most obvious casualties is the loss of doorway leading to the Batcave Service Elevator.
Pilot Study: S01E05: S01E25: S02E01: S02E15: S03E05: S03E11: