Will sodium thiosulfate react with nitrate and/or nitrite ions
First, typically only high concentrations of chloride will interfere with the colorimetric test...I assume you are using NitraVer or something similar? If you aren't using seawater (i.e., $\ce{Cl-} \gt \pu{100 mg/L}$) then you will be okay. But, let's say you are using seawater. There is an easy solution, simply make your standards in an aqueous matrix containing the same amount of chloride. (I hope you are making standards or have a check standard and are not just blindly trusting the UV-Vis result...)

Second, thiosulfate is a reductant and thus could potentially reduce nitrate and nitrite. However, your most powerful answer will be your own tests - you need to do control experiments. Make some nitrate and nitrite solutions of known concentrations and then mix them with thiosulfate at concentrations you would use. Check the nitrate/nitrite concentrations after mixing and determine if thiosulfate reduced them.