How do I get the audio to be heard while playing a video file in an application while sharing my screen in an Adobe Connect meeting?
No, screen sharing is just sharing the image on your screen. It runs at about 3-5 frames per second, which is much less than the 30 frames per second your video runs at. So, even if there was audio, it looks terrible from the participant's experience.
You would want to look at uploading the MP4 to the Share pod or creating a custom pod that contains your application in the room.