No, Re:Coded is a DS port of a cell phone game, KH Coded, that was only available in Japan.
Release order is optimal if you're new to the KH series. Get KH for PS2 to start, or wait for KH HD 1.5 ReMix for PS3. None of the side games replace the original, but each new release of the original has been a little different.
KH, KH-COM or KH-ReCOM, KH2, KH-Days, KH-BBS, KH-Coded or KH-ReCoded maybe, KH-DDD. ReMix 1.5 is slated to include KH, KH-ReCOM, and some videos of KH-Days story (not a playable game). Search up top for "Kingdom Hearts" to find all of those.
Guides and other contributions: http://www.esque.com/slr/gamefaqs/ FFX, FFXII, KH, KH Re:CoM, KH2, Okage: Shadow King, Secret Agent Clank