Im pretty sure Minato already had his students marked from sparing matches.
And Minato mark doesnt go away.
So why didnt he attempt to use SM to track Obitos chakra signature, then use ftg to teleport to Obito using the mark he placed on his teammates?
I dont think Minato was that proficient at Sage mode and Obito left nothing behind for him to reverse track.
For the sake of your argument lets say he could:
Minato had 99 problems to deal with before trying to track Obito:
1) Nine tails was wrecking havoc
2) He was exhausted from the barrier / fighting / teleporting
3) Kushina was exhausted from child birth
4) He wanted to protect Kushina and Naruto
5) He accepted that if he lost the battle (RDS) Naruto would win the war (Jin chuuriki)
6) The other villagers (Hiruzen etc) were playing defensive instead of being aggressive.
So to answer your question. IF Minato was able to recapture the nine tails by:
1) Villagers (Hiruzen and others) offensively supporting him.
2) Him not being exhausted
3) Kushina not being exhausted
He would have without a doubt pursued Obito and eventually found him. Assuming Obito doesn't simply sit in Kamui land until he is fully repaired.
You being pretty sure doesn't equal facts. It's obvious he didn't have them marked there's a reason he gave kakashi the Kunai.
bold is where your wrong and your whole argument falls apart. no he didn't.
The only one that had minato's tag was kakashi via the kunai minato gave him.
I always assumed Minato "Cleans up" marks of either defeated enemies OR after sparring with his comrades to prevent excessive marks. Wouldn't make since to have abunch of corpses marked 6ft under.