Not if sold as an EI flight number, yes if sold as a BA flight number.

You can book London to Ireland returns on the BA website which will sell as a BA flight number and therefore qualify. In the past this would not work and you would only be given these EI flights on a BA number if connecting to some other BA destination. Note that the only fare option is "economy with checked baggage" which will include a 23kg checked item, an overhead and a small carry-on, and a random surprise amount of TPs and Avios. And (in my experience anyway) you cannot select seats, even at OLCI, and will be assigned something arbitrary.