I disagree. NuTrek wouldn't exist any longer, if Nero's ship was blown up before he destroyed the Kelvin. The timeline would have new events from that point onward recorded on it, which would be very similar to Prime Timeline, but not quite. I agree that Prime Universe is overlayed by NuTrek, even though I don't like it.
As far as 1986, I think that until the timeline is changed (by NuTrek ending up in 1986 SF) everything would be as it was... if viewing thru, say, the Guardian, you would see the TOS crew saving whales, then disappearing. I believe that they would not re-appear, since at this point they are physical artifacts/remnants from the old timeline still visible in 1986, but that they would disappear into a void.
The second NuTrek appears in 1986, they are technically creating a new timeline from that point onward that includes their actions. The time artifact/remnant TOS crew is still there. NuTrek's presence (even before blatant interference) should then allow the BoP to come out in the new 23rd century's present.
Its possible, then, that the Probe is still stopped by the TOS crew, while the NuTrek crew and their enterprise is still out in the galaxy somewhere far away. The TOS crew in its 1986 entirety would then be returning to a world they have never seen before, but could continue their adventures in the future of the Kelvinverse.
Interesting.