Ive met a few programmers but I never heard of Rule of Three.
Using consts makes more sense. Yes, it should be Update( const int deltaTicks ), ....but no big deal if you dont use const, but its highly recommented if other people are working on that code too. And you dont have to pass an int by reference when you want it to be const.
Using const in the Update() function like that is useless in this case. The int parameter is being passed by value, not by reference. By value doesn't need a const qualifier because the value is copied, not referenced. You only need a const qualifier if you're passing by reference/pointer and you don't want the function to change the object being passed.
So to answer the OP's last question directly, no. You're not passing by reference there, you're passing by value so the const qualifier is useless.