what if a group of humans traveled from the future stole a stardrive section from the USS Constitution before her shakedown cruise and transported it to the 24th century? What will the timeline and the Federation be like? Oops, I posted it in the wrong section, it should be in the general discussion section.
Well considering that the Stardrive from a previous era were transported to a future one probably not much except a bit longer to construct a replacement. Most likely though the Enterprise was already under construction (if Constitution was 1700) so they may have just moved her stardrive to the Constitution or launched Enterprise earlier as the testbed.
It's not inconceivable that the technologies of the two eras are any different from one another. Despite all the advancements made by the Federation between the time Nero appeared and the launch of the Enterprise the Enterprise was still nearly destroyed in the first volley just as the Kelvin was. Since the Narada was from the 24th Century again probably nothing.
Bringing something forward in time does not affect the future, it is like the P-38 Lightning from WW2 that was found under the ice in Greenland, after suddenly appearing 50 years later airplanes today are no different. Now if you take the Sovereign class USS Enterprise back in time; you will change the past. Give that same P-38 to Orville Wright and who knows how aircraft will be. Also Starships don't just appear; they take years of R&D, Leah Brahms when through how many design changes before she got it right.
The effect on the past technology would probably be small - the Consitiution would be delayed but the knowledge of how to build a star drive section would not be lost. The future would thus probably still have warp drive and technology could have developed along very similar lines, so they would regard the Constitution's star drive as a museum exhibit. What the effect on society and the attitudes of the 23rd centuary people would be is rather hard to say. Do the thieves make it clear they are from the 24th centuary?
What will happen if a group of Humans steal the Federation Constitution? They'll find the secret map to buried treasure, of course! Didn't you see the Nicholas Cage movie Federation Treasure?