The unit of capital allocation in airlines is one plane, and cancelling a flight or adding a new one probably requires some advance notice to airports and other agencies not to mention time for maintenance, flight crews, etc. to ready it or take it out of operation. Then there's pilots' unions etc.
So no, your decision does not immediately affect the number of planes flying, but if many people fly less the net effect will be fewer planes in the air after some time delay.
ive ridden on many long intercontinental flights where a huge amount (almost half) of seats were unfilled..