Does the MacBook battery cycle count reset when replacing a battery
The cycle count is logged on the battery itself.

I've never actually dug into the idea to see the method or technology used to store the cycle count, however I do know this to be true thanks to personally refurbishing hundreds of MacBooks.  When checking over a MacBook's battery life in System Information / System Profiler I would often switch out batteries and check again, deciding if a battery replacement was worthwhile.  Once the battery is switched out you will see the cycle count (along with capacity, etc) change.  If you don't see it change then you either need to refresh System Profiler (command + R) or the second battery just happens to have the same info.

If you're curious you could always visit the Genius Bar at an Apple store and have them pop in one of their spare batteries that they use for testing.