Yes, it's possible to bring down the wall so that you're in the timeless and egoless state that K describes, but can also think whenever you need to, and then stop thinking. In ordinary life, thinking gets out of control.
I have doubts that the usual methods of meditation actually do this. They're healthy exercises that help you relax and clear your mind, largely because of all the deep breathing, but the premeditation and practicing shouldn't be necessary for a mystical experience.
I find that the environment surrounding you also plays an important role. When I'm close to nature, surrounded by an open, welcoming, non-judging community, where each individual feels free to express themselves without trying to conform to any expectations, I'm by default a lot closer to this desired state of mind than in my everyday city life, full of depressed, angry, rushing people trying to live up to certain customary and imaginary expectations.
In this sense, I believe our misguided society plays a large role in constantly rebuilding that wall. Otherwise, meditation might not even be needed.