Nope, that isn't what happened.
Since this scenario is being linked with gaara and co, lets get some facts straight.
Gaara held susano down via the arms with his sand, then ripped madara out. In this case we saw clearly that susano was stationed and it was at the exact location after madara had been ripped out.
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We got the first taste of hiraishin's power but also its limitations.
Here;
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"It won't work unless there's direct contact with myself or my chakra"
What happened in this chapter is that naruto latched onto minato and sasuke and this allowed minato to teleport as there is direct contact with himself and his chakra via naruto's chakra arms or what not.
But my question is this. If minato separated susano from the user, surely it should be a similar situation like gaara's where we see the susano at whatever stage it was in, still being at the location when this occured.
Yet while in gaara's we saw this difference, in this chapter there is no susano at all to state that, he did indeed separate the two.
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Both, Susanoo and the user (sasuke), disappeared. Fact.
There is no susano near obito, if minato did indeed separate the two.
Ill show you something that is even more clear.
If you look at sasuke's susano you would note that, in the upper image it has a flare of susano
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At the bottom page, the whole of susano left along with the user, apart from the little flare outside of susano
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He teleported susano and the user