If you live in Ireland, you are *not* resident in the United Kingdom; Ireland is a different nation, despite a common history and a common travel arrangement. Travel to the United Kingdom establishes a presence and a connection, but you have to meet the residence requirements in order to apply for citizenship.
If you meet those requirements -- for example, if you've had ILR for a year, but just moved to Ireland 2 weeks ago -- then, yes, there is nothing to stop you from applying for British citizenship. You could even apply at the British Consulate in Dublin.
If you don't meet the residency requirements, they are allowed to exercise discretion up to a point. (This is explained in the residency requirements section of the Form AN guidance notes.)
However, if you do *not* meet the requirements and you also do *not* meet the discretionary limits, then you will not qualify for citizenship.
If you submit an application and fail to tell them that you have been living in Ireland, **this will be considered fraud**. They might or might not find out, but if they did, your application would fail, and it would cause problems for later applications -- or, if they found out after granting you citizenship, you could have your citizenship stripped. I don't think it's worth the risk.
