Is that enough backing?

Look no further than the end of your line for the answer to this question -- meaning, check your tippet strength.

If you are using 6X and you have a large fish on, you will not be able to horse him in, right? Therefore your drag is going to do some overtime and thus you may see some backing. If you have some heavier tippet or leader strength so that you can "put the rod to him" and prevent the fish from taking out your line, you probably will not even see your backing.

I sometimes instinctively feel that "the stronger the fish the more backing needed". However, I am always reminded that even if I'm fighting a 40 inch pike or a tarpon, I'll be using heavy leader on these fish. Therefore, I don't need to give the fish much line if I choose, as opposed to using a light tippet where the fish is going to have his way and take me to the backing.

There are certainly exceptions to this rule when fighting fish that weigh more than the average human being. But you will "feel" the answer to the backing question when you switch from 6X to 4X and you are on a big river with healthy trout.