I started out just like you. I am an After Effecsts motion designer. Adobe Edge Animate is an excellent tool and I think you will be impressed with what you can do already in the program.
To answer your question, yes you can "use" Quicktime but I would recommend using .mp4 extension and h.264 compression. Try to reduce files to as small as possible without effecting quality.
Unfortunately, at this moment Edge does not accept video files natively in its system. However, there is a work around for that and it involves some code. Don't be frightened by the code, I didnt know a thing about it when I started about 6 months ago. If you can tell me more about what you are trying to do I can help you get a video file into edge and make it interactive.
Also note that using "just" an h264 encoded mp4 video file will not play back in Firefox. Also note when designing your interactivity that animation will not autoplay on iDevices (iPad, iPhone). There are decisions the browser and hardware manufacturer made, that make it extra "fun" for web developers.
Also note that, as Adam said, there isn't much out of the box support for controling video in Edge. But you can track down code snippets that will allow you to jump around to cue points, swap movies, control volume, etc.