When you make a scientific hypothesis about something that exists, be it a unicorn, a quark or a designer, you are assigning properties to it, properties that can be tested. A thing that can do anything or everything cannot be the object of scientific investigation. If it has no limits then you can't propose a situation where its actions can be distinguished.
Sure you can. If you can rule out all causes for a phenomenon that aren't of an omnipotent nature, then you're left with one choice.
That's of course even assuming that ID theory posits an omnipotent designer, which it doesn't. It only posits an intelligent designer - one that can act with foresight.