For the most part, yes. Every Spinda has a random personality value that determines the coordinates of its four spots; some of these spots may overlap or lie entirely outside the sprite boundary, resulting in fewer than four spots or spots that are non-circular. While this random value is retained when transferred to later generations, the exact size, shape, and relative position of the spots changes slightly each generation. In most cases the difference is negligible and the pattern is for all intents and purposes identical, but in some cases the change in size and position can cause previously invisible spots to become visible after transfer to a later generation.
For example, the default Spinda pattern with a personality value of 0 has a single spot on its forehead (and a tiny sliver of a spot on its left ear that you can't really see unless you zoom in); the other two spots are completely invisible. If you transfer this Spinda to gen 6 however, one of the missing spots is shifted so it is now visible on Spinda's right ear.