Yes, this post is 5 years old, and even though I'm on one of the latest version of C2, it also helped me figure out why my sprite had delay before moving even tho the "Rotate" parameter is turned off. Thank you very much !
So what's happening is, by default, there is a slow rotation used, and even if you set "Rotate object" to No, when telling the object to move along the path once it's been found, your object will still do like a ghost rotation, and that's what's delaying the movement.
You can do the test by setting a slow rotation speed, then Enable the rotation, and if you tell your sprite to go left, then right, you'll notice it's taking its time to rotate, and that's what's causing the delay.