No need to keep them in a file geodatabase either. In fact I suggest not to. I keep all my locators in a shared drive folder called (wait for it...) Locators. And yes you can point them to your sde data. Just remember, that any edits will not be reflected in the locators until you rebuild the locators. If you publish any of them, that means stopping the service first.
In my particular situation, the published locators are used by 9-1-1 dispatchers, so I have an A and B set of locators. At any given time, one is 'hot' and the other 'not'. That means the dispatchers are using the hot one. I shut down the not one, rebuild the locator(s) and then toggle the users from what they have been using to the one with fresh data. So what was hot is now not and vice versa. I then go the the rebuild process again so I'm always up to date on both...
That should just about do it....