Yeah DEFINITELY NOT.
But again Tabata-sensei seems to know what he is doing
unlike THAT MAN
And even if it goes in that direction, It would be an exponentially more tolerable and understandable situation than Naruto's obsessive need to "save" Sasuke for two reasons:
1) Asta and Yuno are actually best friends, not "rivals that are begrudgingly learning to accept and respect one another, making tentative steps towards a friendship". Unlike Kishimoto, Tabata has never tried to force feed a contrived narrative because he demonstrated, rather than just told us, that the two of them were best friends through their frequent interactions and shared history together. Tabata never had to convince us of their bond because we could see it for ourselves. However, If Naruto didn't explicitly state that Sasuke was his best friend, would we ever have assumed that they had that kind of relationship based upon their past behavior? No, we wouldn't. We would just label them as strictly rivals.
2) If Yuno turns against Asta, it's because he is either being brainwashed or possessed because we've seen that Yuno is a righteous and loyal individual. Sasuke's decisions to betray his village, murder his "best friend"and former teammate, destroy the Kages, etc were of his own volition. Frankly, it's easier to empathize with a situation when the hero is trying to save a loved one who's clearly operating against his will than a protagonist that is forcibly trying to "save" someone who voluntarily betrayed them, attempted to murder them on several occasions, plotted to destroy their home, tried to kill their lover, then plotted to take over the world, without showing any hesitation or remorse on his end at any point in time.