Since the domestic connection is booked as AA-marketed flights, it's in B class and you're guaranteed to not get EQM/EQS/EQD for those.
On the IB-marketed flights, it really depends on whether AA's automation is smart enough to pick up that you have a Basic Economy fare. My belief is that it earns according to an O-fare on the IB chart, but I haven't seen a data point of that.
AA.com is telling you that you won't earn elite credits -- I would assume that you will not and then be pleasantly surprised if you do.
Thanks. I'm in the process of trying to cancel it now... IB's support is... well lets just say the AA gold desk actually answers the phone... not sure the same can be said for IB...