@MCDU2 If IAG bought Aer Lingus, it would not be merged into BA. It would remain a separate operating subsidiary. I don't know what that would mean for staff travel rights across IAG subsidiaries.
Whenever asked about whether IAG is interested in buying more airlines their response is usually "we're not interested in anyone at the moment" and it has in its short life bought bmi and Vueling.
I can see some attractions for IAG, namely the LHR slots and the transatlantic potential. However, this is not quite as game changing as bmi or Vueling. Also as Aer Lingus and BA both serve LHR-DUB a potentially material number of Aer Lingus slots would have to be divested to any willing new entrant on the LHR-DUB route.