Well, the OP is going to have to weigh in here, but it sounds as though s/he is referring to one
of the handful of airports with Amtrak stations: Newark, BWI, Milwaukee, Burbank. (am I missing any?)
In every case you have to take a secondary mode of transportation from the Amtrak station
to the terminal. In most cases this is a free shuttle bus (except Newark, which is a "tram").
Generally luggage carts are not permitted on buses and trams, so in all likelihood the answer
to the OP's question is "no."
In Burbank you can walk from the Amtrak station to the airport terminal, but I can't recall
offhand if there are luggage carts available.