Although these sentences are nearly always translated as questions, the (admittedly informal and possibly colloquial) usage of っけ followed by か suggests that there is a difference at least on some level. In my experience, "questions" formed via the っけ particle are often rhetorical -- but just as often, they are interpreted as a request for information.
Basically though, the answer is yes, use of っけ to indicate an attempt to recall information pretty much always turns the sentence into a question.
Edit: Although I believe that this is implicit in my original answer above, I though I would more explicitly answer your question post-edit.
It is not so much that っけ can only be used with questions, but rather that it turns sentences it is used with into a question. For example, consider the following:
- あなたの名前は何でしたっけ。 (warning: this is probably a bit rude.)
This is an example of っけ being used on a sentence that is a question-form (i.e. it uses an interrogative, in this case 何); but it doesn't have to be, as in the following examples.
In these sentences, っけ is indicating that the speaker cannot recall what state he or she is in; by saying this, he or she is implicitly requesting the listener supply that information, which is to say that っけ is turning the sentence into a question