Double DES meet in the middle attack: probability that wrong key pair remains
Yes your argument is correct, to an excellent approximation. 

The reason I say approximation is that the second search in the sample space should really be conducted in the restricted set of DES permuataions that already map $P$ to $C$ (sampling without replacement) but for such a huge sample space the inaccuracy due to not doing this is likely much much less than the modelling step of assuming DES is a pseudorandom permutation.