yes, you did ask that question and, no, there isn't enough information in the earnings report to be able to say whether AE is profitable or not.
Given how closely intertwined mainline and regional ops are, it is very difficult to even be able to determine that - and even internally, costs and revenues of a wholly owned subsidiary like AE can easily be allocated to change the equation.
It is also true that AE's fate is closely tied to AA's overall market strength in its hubs given that the overall ticket revenue affects what gets allocated to AE.
AE will be able to reduce some of its small RJ flying because of BK rejections but still has a large 50 seat RJ fleet which severely affects economics.
AE is probably not in the worst situation but it probably isn't in the best situation either relative to their peers. How close to either extreme they are may or may not make a difference in their long-term future.