EASA can never have membership of ICAO but then again neither can the CAA or FAA. Membership of ICAO goes to the contracting state and not to any body that they have established to meet their obligations under the Convention.
The FAA is part of the US Department of Transportation of the US Federal Government. Presumably national CAAs in Europe are likewise part of the national governments of States that are ICAO members. As such they negotiated and made international agreements between themselves through ICAO, and they continue to do so. EASA is not at the table.
One hopes that the EU Government is not entirely sophomoric.