Yes convictions exist, at least in the USA.
This answer is with respect to the USA, not Ireland or the EU.
I seem to recall in the late 1990s a Vice President for an early search engine company that no longer exists tried visiting an online underage sex-chat friend in person on Santa Monica Pier. He encountered a policewoman. I recalled something about the it was an adult woman's naughty fantasy and there was never an actual child defenses. Memory being fallible, I thought these defenses failed and that he was convicted.
A wikipedia page and this law review article says he was aquitted:
PROSECUTING CYBER-PEDOPHILES: HOW CAN INTENT BE SHOWN IN A VIRTUAL WORLD IN LIGHT OF THE FANTASY DEFENSE? by Donald S. Yamagami
seems to mention the case in the opening page.
The article also mentions that internet pedophilia cases have a remarkable 95% conviction rate.
Stings involving vigilantes or law enforcement posing as imaginary 12-year-old girls were common in the USA for a while, and even featured on a prime time TV show. 600+ convictions are claimed by one vigilante group alone.
Perverted Justice [warning: disturbing material, not-safe-for-work] initially was a vigilante group that began working with the police. Later, the prime time national American TV news/infotainment show Dateline NBC partnered to create a special series "To Catch a Predator" that featured videos of the stings of dozens of suspects.
People from all walks of life (e.g. medical doctors, soldiers, schoolteachers, firemen, and many others) and all mental states from sober genius to mentally challenged to drunk/stoned would show up to claim their "prize" at the house containing a PJ volunteer portraying the girl (sometimes boy) home alone and Dateline star Chris Hansen and his camera crew waiting in the background. Some suspects believed Hansen to be the father or a police officer rather than a TV personality, and Hansen would always tell them at then end of the interview that they were going to be famous and appear on a national TV show. He would then let them walk out to experience their fate being arrested by police.
I don't know if PJ is still active. While their website still exists, the front page shows cases a few years old. They were known for keeping detailed information on their cases, including chat logs, court documents, and convictions.