Theoretically yes, but not a good idea.
Flash, for all its security issues, is everywhere (except Apple machines). It is installed automatically with Firefox and CHrome. It just “works” out of the box.
Quicktime, on the other hand, is a heavy pig of a client. Even the plugin is heavier than Flash. It needs to be downloaded (which most people don’t know how to do) and installed (which is a pain in the ass). And it is processor heavy. Basically it is a big fat client that does only one thing.
So if you want to alienate people who are using your website and force them to use extra steps, then by all means use Quicktime. If you want to make it easy to view your site, then use Flash.
But why use either? Why not make your site in HTML5 and use some the media streaming and delivery mechanisms built into HTML5? Why not use some of the newer streaming protocols like M8?