No, this is not possible. It has to be noted that Konjunktiv II just serves as a marker for indirekt speech here, it could be "wollest" as well or even "dass Du einen Anfall haben willst". Wollen therefore does not gain a special meaning here.
Wollen cannot be used here as the events can neither be wished for nor can they happen by intention of the subject, but wollen has exactly that meaning.
It is possible for wollen to be used for events which just happen, such as "Es will Abend werden"; however, I'd say that this is still different from Es wird Abend werden. It is even possible with an Akkusativ too:
Die Mauer will nicht aus den Köpfen der Menschen verschwinden.
We had that example a while back. This is definitely separate from werden:
Die Mauer wird nicht aus den Köpfen der Menschen verschwinden.
Wollen means here that it is a long process, that the wall seems to resist, but werden means that it will never happen. Therefore, there is a clear difference between wollen and werden.
But why is this possible in the first place? Well, wollen is used as a metaphor here; the wall is an alias for the people which have not yet fully mastered to overcome the estrangement between East and West Germany.