Yes, you can. Weirs make it more aesthetically pleasing and allow for pipe shapes that lower the volume (sound, not amount) of the water going down the pipe without lowering the water level in the tank, but they aren't absolutely necessary. Weirs also spare you from draining the entire tank if the standpipe separates from the bulkhead, but obviously you can just silicone the pipe in and not really have to worry about that. If you're keeping large fish, I'd strongly recommend doing so.