If I book a flight on American Airlines, but it is paid for by my employer, do the AAdvantage benefits still apply?
Specifically the priority boarding and no fee for checked baggage at the airport.
The airlines don't care who paid for the ticket, they award frequent flyer miles and apply benefits to the passenger based on the fare purchased.
Your company could have policies against claiming frequent flyer benefits on company paid for tickets, but that is between you and the company.
Some companies have negotiated fares with airlines and some of these discounted fares do not earn miles.
YES. The program benefits go to the member. Who pays is not relevant.
If you are Gold or higher, you will get Priority boarding and a complimentary baggage allowance.
Additional information: For many years now, all travelers are treated the same, even US Government, for program participation. The only exceptions now being special group fares that earn fewer or no miles/points.
The programs have made policy changes the make it harder for other entities to claim the travel's benefits, not impossible, just harder. At the same time, they have introduced corporate programs to reward corporate payers such as Business Extra.