No. You may qualify for a payment under this Agreement and still claim a payment from another EU State under the EC Regulations on Social Security. This means that you could qualify for a pension from another EU State and a pension under this Agreement.
However, you cannot claim two Irish pensions, for example if you qualify for one based on a combined contribution record under this Agreement and another based on a combined record with another EU State under EC Regulations. Instead, you will receive whichever Irish pension is greater.