Yes, but the specific type of irony that this situation fits the definition of does not come from whether or not the tool they used worked for the intended purpose. The irony comes from the fact that they are relying on the output from LLM-generated content (ISBN checksum calculator) to determine the reliability of other LLM-generated content (hallucinated ISBN numbers).

Irony is a word that has a somewhat vague meaning and is often interpreted differently. If the tool they used did not work as intended and flagged a bunch of real ISBNs as being AI generated, the situation would (I think) be more ironic. They are still using AI to try and police AI, but with the additional layer of the outcome being the opposite of their intention.