No, that's not what I mean by 'falsifiable'.

That there exists some external force or entity that is completely outside the realm of anything observable is not a falsifiable claim, because there is absolutely nothing we could ever observe that would absolutely contradict it. It is, quite simply, not a statement about the observable universe, so it's definitionally outside the domain of science. Science will never disprove the existence of Heaven, because Heaven is by definition not observable.

That's a very different kind of claim from "If you'd sneakily observed Jesus' crucifixion and followed him as he was buried, you'd eventually see him come back to life, move a stone away from his tomb, and wander up into Heaven after having a few chats with friends".

To be clear, I'm not saying that those religious claims have been absolutely proven false, only that they hypothetically could be proven false. Of course, there are other religious claims that have been proven false, like young earth creationism, but those have a funny habit of being either abandoned or significantly re-interpreted after conflicting facts come about. It's also probably just a coincidence that the more fantastical claims all tend to be from long enough ago that gaps in the historical record provide a significant amount of fuzziness. Why God got tired of performing miracles after the invention of the camera is just one of those mysteries.

It needs to be emphasized that I am not making the absolute positive claim that Muhammad never flew to Jerusalem. What I'm saying is that someone with sufficient information could possibly make a clear determination of the truth. Muhammad himself, for instance, presumably knew the truth of the matter. It's falsifiable in that it could be falsified given sufficient observed information, unlike the existence of Heaven, which categorically cannot be.

(It's also worth mentioning that the Qur'an itself actually contains only the slightest and briefest mention of the Night Journey; the story is greatly expanded upon in the hadiths, which he himself did not directly write but are rather traditionally attributed to him).