My wife and I just used two of our admissions at SEA. We were flying out on American and the participating lounge is Alaska's, which is in the same concourse as the American gates.

So, in our case, SEA was airport A and even though we were flying on a different airline, we were able to conveniently use the lounge. We had already gone through security and the lounge was on our way to our gate. We were not asked to present any boarding passes at the front desk.

If we were coming into SEA, then that would be airport B in your question. We would still be able to use the lounge, since we pass right by it before we exit the secured area of the terminal.

Unless some lounge attendant decides to ask for boarding passes (which we never have been) you should have no problem getting into the lounge whether you are departing or arriving, no matter your airline.

It should go without saying that you DO need your Lounge Club membership card to get in.