As it is late any my phone hates me, I will make my point brief.
Iberia would not affected much due to BA and IB having different markets. How many UK airports did IB serve before the sale? Never many. How many does EI serve? A hell of a lot more than IB anyway. Why BA would want to jeprodise their UK and Domestic traffic is beyond me.
If BA wanted a second airport for its TA traffic, it would use Gatwick or Glasgow/Edinburgh, not Dublin. Dublin is a very worrying competition for BA and they are growing fast.
My opinion on what BA may do is they would mess with the schedule of the T/A flights or the UK flights if possible to make them far less attractive to transfers. T/A routes may be downscaled due to lack of passenger Demand and certainly would not grow anymore. Instead of going to Dublin, many English passengers would instead drive/fly to Heathrow and further increase the loads on BA' flights.