No!
If you are entitled to a payment under this Agreement, this
will not affect your entitlement to a payment by another
State under the provisions of the EC Regulations on Social
Security.
This means that you could get a payment from another State
under EC Regulations and a payment from Ireland under this
Agreement at the same time.
This could arise if you had been employed in the United
States, Ireland and another country covered by EC
Regulations.
However, when working out a person’s entitlement to a
payment under this IRL/U.S.A. Agreement, work periods
completed in the other country covered by EC Regulations
will not be taken into account.
You cannot claim two Irish pensions. For example, if you
qualify for one based on a combined contribution record
under this Agreement with U.S.A. and another based on a
combined record with another EU State under EC
Regulations, you will receive whichever Irish pension is
greater.