Just got off the phone with John G. We spoke of both the metallurgical and practical aspects of case hardening and coloring. The gist is as follows.
Metallurgically, annealing before re-case hardening is not necessary. All hardness is lost when the metal temperature goes above critical; the metal has no "memory" of hardness. Practically, most parts will require some amount of polishing/pit removal/re-engraving which will be vastly easier to do after annealing. Further, a part retaining the original "skin" hardness is more likely to be filed/ground/polished in a way that leaves the "skin" thickness uneven - remember that case thickness is on the order of 0.002" - 0.003". Re-casing will increase the "skin" thickness and surface carbon content. But, it will not completely even out the thickness. Thinner parts are more likely to warp from an uneven "skin" thickness.
Warped parts can generally be bent back to working dimensions due to the core softness of the metal and the thinness of the hard "skin".
Repeated case hardening cycles will produce poorer colors due to increasing carbon content at the surface (high carbon steel is more resistant to oxidation than is low carbon) and thicker "skins" that are more prone to warping and to cracking. Smaller/thinner parts are more subject to this than are bigger/thicker parts.
Modern alloys can generally be case hardened without through hardening due to the higher critical temperature of such alloys. Also, those parts that are through hardened can be case hardened and colored without loss of all through hardness as case hardening/coloring temperature is around 1250 degrees F.
Oxide colors can be restablished at temperatures in the 700 degree F range. John tells me that some of the CC colors do not appear in oxide coloring and will be absent unless the part is heated to the afore mentioned 1250 degree range and submersed in casing material. He should know better than I do.
In sum, most parts will need to be annealed prior to re-casing. Warping is a fact of life and not the end of life. There is a very finite number of times a part can be re-cased; for very thin pieces that may be only one (the original). Oxide colors can be re-established without rehardening, but true CC can only be re-established via re-casing.
Hope that helps some.