So a lot actually happened in that interval from warp-out to arrival. The Narada could have totally done that much damage to the fleet in that amount of time... especially considering that the Narada had late 24th century weapons.
That is probably true. However, there is no reason why it SHOULD be true. I think the point that the OP was making was that the Enterprise went to warp a very short period of time after the fleet. If Pike followed the same procedure i.e. speed as the others, he would have arrived the same amount of time behind the fleet.
However, given the short amount of time after the fleet he left, he could easily have teased a bit more out of the engines to catch up. If he didn't, it was because the emergency wasn't considered that much of an emergency. If it wasn't that much of an emergency, why did the fleet take the risk of warping all the way inside a planetary system.
1. Even at high TNG warp it should have taken the fleet between a day and a week to reach Vulcan.
2. The fleet should have warped to the outer edge of the system and then used maximum impulse to reach the planet in a matter of minutes. Thus their scans should have been able to warn them what was going on.
3. It isn't clear what the jamming range of the Narada was but the fleet should then have been able to send a signal to Earth, Pike, and the Laurentian system or send one of the ships out of jamming range to do so.
4. None of the ships should have engaged without shields up (it would also be insanity to warp inside a planetary system at warp speed without shields up).
5. Pike would have arrived at most before the rest of the fleet engaged the Narada.
Overall, the set up was a bit dumb but luckily most people just take the scene at face value. Examine it too closely and it is ridiculous.