Certainly. If you can play a video in Allegro, than you can show it anytime you wish.
How and when is up to you. Maybe when you create a level, you can add certain flags to it. If it was say, a tile map, certain tiles could make marked to show a video if the players moves over them. For example, lets say you have a 2D map with a bridge the player must cross, but if they cross a troll appears from under the bridge in a video you prepared. The map itself consists of 2D tiles, so you could mark one of those tiles as a trigger for the video clip. In your game you would have a tile struct which would have a flag which could indicate if that tile is a trigger, then another one which indicates the trigger type, like a video. Then another variable which contains which video to play, maybe a filename etc.