If you put two atoms A and B in an box and wait 1/2 of the half life, then the probability that the atom A survives is 1/sqrt(2). The probability that the atom B survives is also 1/sqrt(2). So (assuming independence) the probability that both survive is exactly 1/2. So you are right!

(I'd prefer to say that it's a property of the exponentially distribution, not the Poisson process.)