Hrm. In broad terms, yes; more phosphor restrike will probably both lower CCT and increase CRI. This isn't due to any special magic of restrike, it just further masks the blue spike inherent in white LEDs by producing more of the phosphor output. Since the phosphor glow more-closely resembles the characteristic bell-curve spectral power distribution of black-body sources than does the blue LED's output, the CRI is likely to increase. However, a properly-designed high-CRI LED will probably give you higher output than a de-domed cold-white LED. There are also other ways to enhance restrike than carefully slicing LEDs up.
(Wiki spectral power distribution)
(White LEDs are just blue emitters with phosphor on top that down-convert blue photons to lower-energy red/orange/yellow)
(Most high CRI emitters are still missing much turquoise output)