This is slightly outa left field, but when I was younger, I remember all these movies/shows about people from the modern era in the future (Buck Rogers, and some show by Rodenberry where the hero was 'Dylan Hunt', a scientist from 1970), where their 'primative' knowledge and 20th Century sensibility helped them save the day time and again.
I would imagine someone from the TOS era would almost have a leg up on DW era SF characters, coming from a time with more threats and enemies. Sure he wouldn't know a quantum flux regulator becon from a self sealing stem bolt, but when the gagh hit the fan, he would be more willing to reach for his phaser than the SF negotiators manual.
I think there would have to be adjustment time; the tech would be intimidating, but the interface on most Fed equip is user friendly. Understanding the galactic politics and assimlating the history would be more daunting.
Also, think of the change in the world view; coming from the out of the Cold Warish TOS era to the very hot war of the DW: It would be like taking a miltary officer from the 60's and putting him into the frontlines of the War on Terror. (Imagine finding out the enemy you spent your whole life preparing to fight are now allies, while your own nation was attacked by people you didnt even know existed, and now your in a war in a place you've barely heard of...)
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"Yes, it's the Apocalypse alright. I always thought I'd have a hand in it"
Professor Farnsworth