No, that statement is not true. There is no cultural or widespread practice in Ireland or anywhere else where people use medical syringes to remove their own blood and then inject it into their breakfast sausages to consume a part of themselves.
The idea you mentioned seems to be a fictional or misleading account. It is crucial to be cautious about spreading or believing such misinformation without any credible sources or evidence to support it.
Traditional Irish breakfast typically consists of a combination of bacon, sausages, eggs, black and white pudding, tomatoes, mushrooms, and toast, among other items. There is no ritual or custom involving self-inflicted blood extraction or the incorporation of blood into the breakfast sausages or any other food items.