OD600 measures both the absorbance of the medium and the turbidity of bacterial suspension. So we usually use fresh medium as blank to subtract the absorbance of the medium. At the presence of pigments, OD600 also measures the absorbance of the pigment. The intensity of absorbance depends on the absorbance wavelength of the pigment. For example, the violet pigment has strong absorbance at 600nm, while red pigment has less. Three options you can do. First, spin down cell pellet and use cell-free supernatant of old culture as blank. Second, re-suspend the cell pellet in fresh medium and do OD reading, but there may be still some pigment left. Third, use other wavelength between 500 to 650 that people often use to measure bacterial density but has minimal absorbance of your pigment..

The OD600 is a turbidimetric assay. Consequently, it determine the density of bacteria in a medium, but you don't have any information on the bacterial viability in the medium.

In your case, if the coloration generation is not toxic for the bacteria it is OK. If it is toxique, the best way to assess the number of bacterial is to number them at different time by platting serail dilution.

The answer to your question may be yes. To confirm that you need to have a wavelength scan around 600nm or nearly full visible light scan with aspectrophotometer. For best sensitivity ideally you should not have any significant absorbance at 600nm. With your coloured media you may still be able to measure them as blank will subtract the absorbance, however, you will have to compromise on sensitivity but in practical this shouldnt be a problem as usually the working OD is higher (~1.0).

Alternately you can simply spin down the bacterial culture and wash it twice with PBS and then reconstitute with PBS. Now measure its OD600 against PBS as blank.

Hope that makes some sense. Goodluck!

It is not recommended to add pigment as it gives you wrong absorbance, wave length 600nm is effective for microbial turbidity

Actually, it is good to use the pigmented supernatant as the blank. But OD readings have to be correlated with colony counts on plates to get a better idea. While removing samples for OD, a little of it could be diluted and spread over a sterile media surface and the colonies counted. But this might be time consuming. So one could also check the diluted culture under a haemocytometer for the density and express it as (cells/ sq mm) and correlate the same.