If (and it would seem unlikely) IAG were to be able to acquire Aer lingus, and retain all those LHR slots, then I guess is they'd slim down the Dublin transatlantic operation, and use the newly acquired LHR slots to add yet more capacity to the London / USA routes. I can also see BA using EI as a feeder operation to their LHR hub mainly, and cutting down massively on direct DUB - mainland Europe destinations, treating Dublin as it does Manchester, Glasgow and Edinburgh.
While I suspect you are right, let me present an alternative business model.
BA currently operate a lot of flights between the UK regions and Heathrow, particularly Edinburgh/Glasgow. Most of these passengers are connecting on to long haul flights, with US destinations being amongst the most popular.
With the acquisition of EI, they would gain an additional hub in Dublin, which is ideally located as a transatlantic hub. With the ability to pre-clear customs and immigration in Dublin, it becomes an attractive alternative hub for regional passengers. If enough can be tempted to connect through Dublin, then they can reduce frequency on regional flights, freeing up slots for more long haul.
The same approach would also work for European destinations - why fly France-LHR-US, when you can instead route through Dublin and pre-clear? This would free up yet more slots for longhaul at LHR.
With the saga over the 3rd runway at LHR continuing to drag on, BA needs a backup plan for expansion. This could be perfect.