Yes. Simply put, this would never happen, mostly due to personal reasons.
Firstly, Trotsky and Stalin didn't yet hate each other during the Civil War. Sure, they were catty towards each other (Both were arrogant pricks, only Trotsky had a superiority complex whereas Stalin had an inferiority complex), but it was really only after the Polish-Soviet War that their relationship started seriously going down hill, and it was magnified a thousandfold after Lenin's death and their competition (if you can even call it that) over the mantle of succession.
Which leads to my second point. Both before and after the debacle at Warsaw, there were only two people allowed into Lenin's presence without appointment and at any time; Trotsky and Stalin. He valued them both immensely, Trotsky for his military genius and intelligence, Stalin for his brutal pragmatism, equally brutal competence, and out-and-out brutality i.e. willingness to do dirty work.
The idea that Tukhachevsky could just court martial Stalin for his poor performance is ridiculous; Stalin was far too influential, not yet hated, and if that isn't enough, Tukhachevsky can count on swiftly getting a bullet in the back of his own head for killing off one of Lenin's favorites.
With regards to the theory about a stronger military presence in Soviet politics, well that's also a bit dubious in my opinion. The Party was always aware of the threat the military posed to its complete control of the State, which is why it was never shy about shooting officers and one of the primary reasons for the introduction of political commissars into the armed forces. The military could never be allowed to be in a position to threaten the absolute dominance of the Party. Ever. So, the first whiff of that they get and you'll suddenly see a whole lot of officers making sure they've never got their backs turned to their political commissars.
Concerning Tukhachevsky, he's pretty much doomed any way you look at it. While average soldiers liked him, he was greatly disliked by both the Party and military hierarchy. Both constantly undermined or outright ignored him and his orders during the wars. Tukhachevsky, being brilliant and knowing that he was brilliant, responded by being just as nasty and dismissive towards them; the only people who really liked the guy were commoners and his own troops. That, added to his own dubious ideological purity, made him dangerous to the Party, and no matter who came to power they would have to deal with him. Stalin, being Stalin, had him shot. Kirov probably would have done the same. Trotsky or Rykov or somebody else probably would have just "transferred" him to some position roughly equivalent to overseeing the maritime border between the USSR and Mongolia.