Short answer: Yes, the winning probabilities (and expected score) do not depend on the K-factor.  See [Wikipedia](https://en.wikipedia.org/wiki/Elo_rating_system#Theory) for the formulas. 

When you calculate the expected scores for player A playing against player B, you assume the rating numbers to be known. The K-factor enters when you are *updating* the Elo rating based on results from new games.