A couple of points to consider.
Filters remove bugs primarily filtering out the particles that the bugs are living on. Media filters do not remove much below about 10um give or take a bit and many bugs are less than that. Bacteria can range in size between 0.1 and 100um. Ecoli is about 1um long. So a media filter is not a 100% barrier anyway, but probably removes 99% or 99.9% of bugs that are applied. Some get through and that is one of the reasons that we disinfect. There are also many bugs in the system that pose no particular hazard to human health and may or may not be killed off with chlorine. Thats why chlorination is called disinfection not sterilisation.
Running filters at too high of filtration rate, or past the point of breakthrough will increase the passage of bugs.
Most of the bugs are removed from the filters during backwash. This is through two mechanisms. The bed expands and the water lifts the dirt particles from the bed and carries them away. Those dirt particled have various bugs in them and on them. Some bugs that are clinging to the filter media will be rubbed off by the abrasive action of the particles colliding and the stream of water running past the media. But some bugs may be left.
Backwashing with chlorinated water will kill off some bugs no doubt but the contact time is relatively short, no more than a couple of minutes probably and the chlorine residual if taken from the clearwell or a service reservoir is probably no more that 3mg/l if that. However the chlorine demand is likely to be quite high given that the filters have trapped all sorts of stuff including a heap of bugs during the last filter run. So some bugs may be killed off by the chlorine, some will be backwashed out and some may be left behind.
A Google search will soon pull up various research papers on the impacts of having a biologically active filter bed. Usually its considered to slightly reduce the potential to form disinfection biproducts. Whilst some plants report significant reductions others report negligible to nil reduction. Those that report the best reductions usually have unchlorinated backwash, however unchlorinated backwash is not neccessarily a guarantee of such removals. Having ozone ahead of filters with a layer of GAC over the media tend to work even better.
I do process work for a Utility with 9 water treatment plants. We have two that use unchlorinated water and the rest chlorinated. One of the two that has unchlorinated backwash consistently has the lowest DBPs but there are so many things that influence DBP formation I don't think you could point to the unchlorinated backwash and say thats the answer. However it probably contributes.
Regards
Ashtree
"Any water can be made potable if you filter it through enough money"