I don't think so. I am currently learning about Indonesian historiography, and one of the major issues in said field is the fact that precolonial records are mostly commissioned by royal courts and is rife with mythological elements, as well as bias toward the person who commissioned said records.

For example, there are many stories of noblemen who had magical creatures helping them. Of course, historically speaking magical creatures do not exist. However, why did the scribe choose to add a magical creature in their narrative? There are a couple of interpretations.
Firstly, it could be said that the supernatural or magical element carries a certain cultural meaning which the writer attributed to the person. In the case of Biblical narratives; why was the donkey chosen for Jesus' ride into Jerusalem? Was it chosen at random, or is there a deeper cultural context behind the choice?

Then, was there any amalgamation with other narratives which happened, as is sometimes said to be the case of Moses? Why did the amalgamation happen? Did the amalgamation serve any narrative purpose?

If analyzed critically, these kinds of supernatural elements could be a very good historical source for the contemporary zeitgeist of the era when the text was written.

Secondly, mythological feats could be used by writers as justification for a certain act or position of the person they are writing. For example, why did Constantine's Battle of the Milvian Bridge feature a miracle that led him to pick Christianity as the official state religion? Did this miracle disprove the entire battle, or was it added on to give the battle more meaning? It could be argued that how The Miracle at Milvian Bridge was used to legitimize Constantine's rule was as impactful historically as the battle itself.

Thirdly, historical accounts could have actually happened in a different way, with the narrative over it changing more and more as more time pass. Most famously, this is what happened with Troy, as the story was most likely a distorted narrative of a conflict which happened in the Bronze Age.

Thirdly, it could be that the supernatural elements in a story are literary metaphors for something which happened, but were discouraged from being written. There has been a lot said about Mary's pregnancy being a result of mere infidelity, and that the virgin birth was written to 'hide' or ameliorate that supposed fact. Earlier I specifically mentioned Indonesian historiography; it was because the local literary tradition has a rich history of adding mythological elements as a way to cover up or sneak in historical facts which cast the patron of the work in a bad light. For example, the Babad Mangir, written by the rival Mataram Sultanate mentioned that the Duke of Mangir possessed a magical spear which he used to fend of Mataram attacks. Some historians have interpreted this spear as a person of low birth which was "erased from history" by way of damnatio memoriae. Turning them into a spear would 'answer' how Mangir was able to fend off Mataram's assault, while at the same time making sure that the real person behind the attack will be forgotten by any would-be dissenters living in the now conquered territories.

TL,DR: Supernatural events don't necessarily disprove entire historical works. Firstly, it could give a very good window into the contemporary political and cultural zeitgeist, which could be a big historical influence by itself. Secondly, the supernatural elements could also be historical facts which were altered due to the passage of time or for some sociopolitical purposes.

Edit: Thanks for the award and please check out u/Harsimaja 's answer to this question! He was able to describe the 'verification process' of historians, so to say, in greater detail than what I was able to.

I think the point is that historians don’t rely on some magic formula for whether or not a document or account should be entirely relied upon and taken at its word. Everything is subject to being questioned and the more convincing evidence and corroboration there is, the more likely a historical claim will be.

For example, it’s in practice quite rare for Greco-Roman (or honestly ancient) narrative history of any length not to have some honestly implausible stories, often cute supernatural anecdotes and the like, from Herodotus, Plutarch, Suetonius, Josephus, Tacitus, and hundreds of others.

If we have an ancient manuscript, we can regard it as unreliable in principle, but still have to tease apart that someone wrote it, which is not nothing - even the parts that seem extremely fanciful. If common threads pop up in histories that can be argued to be independent, which are specific and would correspond to . We’d probably give more weight to a claim that such and such an emperor who would have been a well known figure died in such and such a place than a claim that an augur saw a bird circle seven times a week before to prophecy said death. The first is at some level mundane and would have been common knowledge, both difficult to make up. The second is both harder to falsify and it’s easier to see the motivation for adding such a colourful anecdote. But we don’t automatically assume it must be true! We assign it a higher probability of being true, and seek further corroborating evidence. If we then notice that other historians say the same thing but with different peripheral stories, and that coins embossed with that emperor stop being made at around that date and occur at a frequency we’d expect for a reign of that length (for example), we assign an even higher probability to it being true, and in practice might ‘assume’ it in conversation after a certain point. Where we don’t have corroborating evidence, a major historical account may at least be worth ‘noting’, and at the very least paints a historiographical picture - and may give some insight into what people then thought, which is itself of interest.

In the end, this is a human field of study, and humans are complicated: rumours, nonsense and false propaganda can pop up for all sorts of complex, human reasons. We won’t have mathematical proof of events or algorithms to determine truth, but there are many more precise methods of textual analysis, archeological dating, etc. which can provide data, and then (in some ways, just as in the law courts) the process of building a body of evidence is based on arguments pulled from the whole sphere of human experience and fine details will usually be the subject of continual academic debate until (and even after) a reasonable consensus can be achieved.

Religious texts are treated the same way. We don’t robotically argue that a text for which we have copies very close to events must therefore be true (I’ve seen this argued in a Biblical context) any more than we assume that a modern tabloid from the same day as some supposed event must be accurate, especially when there may be well understood psychological, cultural, political, ideological or financial motivations for reporting such stories regardless of accuracy.