You are using concealed carry equipment if that's what you choose to use.
Regardless, if you think learning to get fast hits with competition gear isn't helpful in learning to get fast hits with non-comp gear, then I think you're flat wrong. Your hits with non-competition gear won't be as fast as with your competition gear, but that's not the relevant question. The question is whether the hits will be faster than if you didn't compete. And the answer is very clear. Yes, you will get faster, across all contexts.
Regardless, if you think learning to get fast hits with competition gear isn't helpful in learning to get fast hits with non-comp gear, then I think you're flat wrong. Your hits with non-competition gear won't be as fast as with your competition gear, but that's not the relevant question. The question is whether the hits will be faster than if you didn't compete. And the answer is very clear. Yes, you will get faster, across all contexts.