It's a very complicated question as to whether events pre-2233.04 were affected by Nero's incursion. We've seen interference by relics from deleted timelines in Trek before so it's very possible if Kelvin Kirk went back to 1986, he'd meet TOS Kirk hunting for whales. Data's head should still be under San Francisco in the Kelvin timeline with all his memories up until TOS season 6. ST'09/ID Co-writers Alex Kurtzman and Bob Orci are on record saying everything pre-2233 is unchanged.
"That being said..."
Modern Trek reimagines so much, it's hard to draw the line between what is meant to be the same (Picard, Scotty, Riker visiting classic Enterprises on the holodeck, the DS9 gang visiting "Trials and Tribble-ations") and what is meant to be "the same" (Discovery Klingons, Pike's Enterprise etc). It could be the San Francisco of TMP, Discovery, ST'09/ID, Berman-Trek and Picard are all meant to represent the same place looking in-universe exactly the same just like in-universe Chris Pine's Kirk looks the same as William Shatner's.
Add to that, Star Trek Beyond co-writer Simon Pegg saying the timelines are seperate all the way to the big bang, in an attempt to appease fans who see Sulu's sexuality as a continuity error (yeah right that's why they don't like it

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