No - not usually - but I would advise you to try matching to Aer Lingus. (Depending on what level you might get matched to, you can get a number of free upgrades too from EI...though, of course, many parts of the existing programme are likely to be changed after the takeover).

The Gold Circle club looks like it will be changed, to adopt the Avios currency used by the other IAG airlines, and it will give you oneworld status if/when the takeover goes through.