Complexity analysis of an unsolvable algorithmic problem?
Basically, this is a degenerate case.  We can adopt the convention that the running time of any algorithm is $\infty$ (so its complexity is $\infty$), or we can adopt the convention that it doesn't have a complexity.  For informal conversation, probably it doesn't matter much what convention you adopt, as long as it's clear which you're using and what you mean.

See also how to calculate time complexity of non terminating loops for discussion of the running time of an algorithm that never terminates, and What is the difference between an algorithm, a language and a problem? for background on the difference between the complexity of an algorithm vs the complexity of a problem.