Combining CDMA with differential Manchester-like encoding?
With CDMA everything you would traditionally do with a symbol such as timing and carrier recover still applies- but in CDMA the symbol is the series of many “chips”.

So yes you could certainly add any higher level coding to the symbols where in CDMA the symbol may represent a data bit such as +1 and -1 only (perhaps), but each of these data bits after such coding would then be expanded to the CDMA sequence.

There is no motivation to change the sequence itself other than its cross correlation properties to the other codes used and the overall processing gain required. Timing and carrier recovery is done after despreading.