Not really. For example, following a procedure which behaves well in the long run and provides 95% coverage you could get a confidence interval that contains only impossible values. Consider also the following example: you want to estimate x from two random numbers taken uniformly from the interval[x-1,x+1]. The interval defined by the two random numbers is a 50% confidence interval (half of the times x will be in the middle of the two). However, for some specific realizations (when the distance between the numbers is grater than one) you will be able to say with certainty that the interval contains x. See also https://github.com/richarddmorey/ConfidenceIntervalsFallacy