I don't think so? Myth beforehand is a metaphorical interpretation, usually confirming some narrative founded deeply in culture. Very similar to fairy tales that carry values and cultural messages over generations. As long as you have literature and/or poetry, you have solid foundation for myths.
Your distinction is a little vague, myths are intimately connected to religion in my understanding of history and tend to be forgotten along with the religions that believe in them. Most Norse mythology for instance was lost along with the conversion of the Scandinavian countries to Christianity. There are not many instances when the mythology survived intact but the culture changed their religion, though poetry and literature tends to survive that in general, myths do not.
In Dwarf Fortress, as I understand the dev page myths are supposed to determine how the procedural elements of the world are generated, magic being but one of those elements. Myths are not really cultural in the DF, they are quite objective in their consequences, they decide how the world is, before any cultures exist. The cultures end up with potentially corrupted versions of the one-true-myth that the world has.
Mechanically this works fine for non-magical worlds, it still isn't reality after-all and hence nothing keeps them from having procedural elements as long as these involve no magic/are realistically possible and a story can exist to explain how those elements came about. The question is simply why are they called myths in this setup when that term implies magic/religion/supernatural? The 'true story' is this world is going to have to be secular and scientific, which means it is not a myth; or otherwise it is not a no-magic world.
The problem is that you want to have your cake and eat it too. If you want to convince someone in a no magic world that you are a god, then yes it should be hard and yes it could influence people more broadly. Actions have consequences. If you don't want those consequences then take different actions. You could still start a personality cult or political movement where you are a special non-magical leader.
Or use the magic system to mod in an object with a mind control interaction and remove the magic tag so it appears in a no magic world.
The problem is that your actions in a no-magic world are tightly constrained by your inability to *actually* be anything other than a mortal being. Playing as a personality cult leader (which is what you are doing if you choose your own identity as your worship-front in any world) means the death of that character is the end of the game for that particular *you*. You are no longer able to influence the worship organisation you created ever again. This contrasts with a situation where you play as a god, when your character dies you can start another character and assume the same identity again.
If I create a personality cult in a world without an afterlife, the cult may still survive the death of your character if his ideas and accomplishments remain relevant to the present-day. But your role in this as the player is forever over, you can't turn up and say
"I'm really OLD CHARACTER" because they will just respond
"you can't be, OLD CHARACTER is dead". The only way to not have that is for the OLD CHARACTER to convince people he's a god rather than a mortal, which is a hard thing to do in a world with no concept of gods and the new character to also lie, pretending to be the same fake god profile.
But the technological ascendancy also has another purpose besides allowing you to maintain a multi-character cult. Think of what happens in a world where magic is rare but exists if you declare yourself to be a technological ascendancy, truthfully or otherwise. The successful introduction of the concept into that world will undermine the world's supernatural beliefs, since they could just be
"sufficiently advanced technology".