1) he wasnt the first missionary, just the most sucessful.
2) he really, REALLY didnt want to go back and save the people who had made him a slave. One gets the impression that at the start he might have been just as glad that all irish burn in hell. So it would be pretty easy to have him either not go at all, or to not put his heart into it if he did go.
3) one of the things that seem to have made patrick so very effective is his ability to create parallels and analogies that resonated so effectively with his listeners. The shamrock as a model of the Trinity is only the tip of the iceberg. His coopting of the native intelligentsia into christianity, the bards particularly, but also brehons iirc, was a stroke of genius.
My guess is that without patrick ireland converts a bit slower, and is more roman. The biggest difference may well be that its not nearly as literate, no irish beacon keeping the flame of learning burning in the dark. Without the enthusiasm generated by the grafting of christianity onto the native culture, your not going to get so many missionaries fanning out from ireland to england and the continent. Which means no alcuin of york, which means no carolingian rennaissance, or at least a feebler one.
The effects may well have huge global impact, not just on ireland.
No cooption of nearly as much culture, so no glorious celtic knotwork in thebook of kells. Minimal compared to some of the other stuff, but that world would e a poorer place to live.