Are there specific 'pitch accent' traps I should avoid early on?

I’m a grammar-focused learner, and I’ve read that Serbian has a complex pitch accent system. Some people say not to worry about it until I'm advanced, but I don't want to bake bad habits into my speech now. How important is it to master the falling/rising tone for basic communication? Will native speakers in Belgrade understand me if I ignore the pitch entirely, or will it make me sound completely unintelligible?