No, the camera would not cause that. But a moving camera can cause things to happen, such as objects appearing or disappearing, which could have an effect on the performance.
Honestly, the 59 FPS thing is not the problem. Even AAA games will hover around 58 - 62 FPS because it is not perfect, every frame is doing something different so it's not possible for it to be exactly the same.
The issue is probably with your logic being framerate dependent. If you use the delta parameter (the time of the last frame) and make sure all movement code is based on delta, then it doesn't matter the frame rate.
You could even have a game drop from 60 FPS to 45 FPS to 30 FPS and then back to 60 FPS and there will be no slow down. Granted it won't look as smooth, but there will be no difference in the speed of objects or hiccups.
So you might want to double check and make sure you are using delta and timing correctly, having the right things in physics process and/or process and updating correctly.
http://kidscancode.org/godot_recipes/4.x/basics/understanding_delta/