No. In the past, it was more common to simply die by disembowelment.
However, the method of leaping off the head at the moment the blade was inserted into the belly became more common during the course of time. (I don't remember when... I think it was around the Edo period.)
It's more painless that way.
(My memory could be wrong. It's a statement I made without any source, so it's not 100% accurate.)