There is no need for the future "will".
The sentence as given states a general truth. "Anybody, in this noisy situation, becomes oblivious to the noise." The simple present is good for that.
Note that "You" does not mean "You, the person I'm speaking to" but "a general person". This is the "generic you". In formal speech you might say,
One becomes oblivious to the noise.
If you were speaking to an individual, and wanted to talk about their particular future, then you would use "will".
You will become oblivious to the noise.