In terms of weight, the dropship would be expect to airlift the APC and return to the Sulaco if the mission had gone well. The APC would weigh more than than the Queen. So, it's really not an issue
Notwithstanding that, the dropship is fanciful at best. It breaks so many laws of physics, it sits just outside of Star Wars levels of daydream technology.
As a cinematic experience, it's a thrill ride and visually a cool and convincing looking vehicle. In the real world, however, the dropship is an engineering failure and would not function as depicted in the movie. It's just not possible.
-Windebieste.