Can trainers levels 23 & 24 power up Pokémon to cp 2000+++ or trainers levels 26 & 27 have Pokémon cp 2800-3000++?

Trainer level only restricts the level of the Pokémon, not it's cp. Someone at level 20 can have a Dragonite at around 2K. As a level 26 (almost 27) I can have pokemon between 2000-2200. Even if I had a dragonite it could only be around 2600 at the very highest...

Dragonites, exeggutors, arcanines, and vaporeons have higher than average CP. Would all be very possible, I think you would have to be level 28 to have a 3000 dragonite though. Although I might be wrong about that.

I just hit 3000 at lvl 29, but it is not perfect.

As some of the replies have already mentioned CP is not directly restricted by trainer level. The max level you can power up a pokemon to is 1.5 levels higher than your current trainer level.
At the bottom of each individual pokemon page on this site, there is a CP range listed for each level for that particular pokemon.

A lvl 24 can have a dragonite CP 2550 (100% IV)