Is this true or false? Without vacuum leak, the first few times you pump the brake, you can still get some of the vacuum assisted braking. I'm trying to diagnose suspected vacuum leak in this case.
This is true if there is a vacuum leak in the braking system, if that is what you are asking. You should be able to run the engine so there is a vacuum draw at the assist canister. You can either have a gauge on this to check for vacuum (exact measurement), or you could pull the vacuum line between the check valve and the vacuum assist canister and listen for the rush of atmosphere as goes back into the assist canister. Not a very scientific method, but it gives you a clue.
I think the best method would be to put a gauge between the check valve and the canister and see how the vacuum holds over time. A small leak wouldn't register very quickly, but would show itself over time. A small leak may not be very detrimental, but could be an indicator of things to fail.