to which sourc(es) of Cs-137 does your question refer to and in which part(s) of the Pacific?
In respect to known recent or ongoing instances of Cs-release such as at Fukushima or during 20th century nuclear tests in the Pacific, I do not deem the potential effects you inquire about likely. I think such impacts to be detectable would require more substantial amounts to be released, e.g. point sources of big quantities at very localized areas. The short half-life of Cs-137 (~ 30 a) would also constitute an important aspect of consideration there.