Not quite.

You're fine for all the other majors.

But AA might table or slow-roll your app if you have flow, and they need pilots for the regionals. You'll probably flow when you're supposed to, but they might not hire you early around the flow.

In fact this could happen with any legacy, and has happened in the past. Majors might slow off-the-street hiring from any regionals which fly for them.

Safest thing in this climate would be work for an AA WO which ONLY flies for AA. Then apply to DAL & UAL when eligible, they might actually PREFER to hire their competitor's regional pilots. If that does't pan out, then flow to AA.