Well, not exactly.

What it really means is that the execution time does not depend on the size of input (n).

What it does not say is how much time it takes to execute, whether it is exactly same amount of time every time or whether there exists some kind of upper bound on execution time.

For example, an algorithm that takes 1/(randFloat()) time to insert an element to the data structure where randFloat() returns any possible floating point number with equal distribution, is still O(1) algorithm, even though there is no upper limit on how long it can take to execute.