No, this is not possible. Although you can set the column to begin comparison on, CompletionModels implicitly require a prefix in order to work.

You could implement your own widget to do something like what you require. Doing so will show why it is a bad idea: because you're forced to check every position of every word in your list.

Question: is the user really so incompetent that they can't be counted on to type correctly? Or will type correctly, but precede the correct portion with random gibberish?

Perhaps you should explain exactly what it is you're trying to do. Frankly, it sounds ill considered from what you've presented here, but perhaps a more detailed explanation will suggest a reasonable approach.