Short answer: Yes, the winning probabilities (and expected score) do not depend on the K-factor. See Wikipedia 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.

K-factor does not affect the winning probabilities.

The K-factor enters when you are updating the Elo rating based on results from new games, it determine how big the change will be. When winning\losing a game, A player can gain\lose up to the K factor.

See Wikipedia for the formulas.