How will the degree of conjugation effect the light emitted? (glow stick reaction)
The initial chemiluminescent (CL) species transfers its excited state energy to the dye. This depends on the overlap of the CL emission spectrum with the absorption spectrum of the dye and their spatial separation, i.e. better spectral overlap and higher concentration more transfer and more dye emission. (see Forster energy transfer for mechanism).  The dyes used have 80-100% fluorescence quantum yield, so v. high chance of emission. The intensity you experience will also depend on how your eyes respond to different colours. 

The energy gap in the dyes does not greatly affect their fluorescence efficiency, this is primarily governed by interactions within the dye to produce triplet states which drain energy out of the fluorescent singlet state.