Well this depends on how you render the scene in the first place. Typically games will now render in linear light space to a fp16 backbuffer. This is then subject to exposure control and tonemapping to get this unbounded HDR image into an LDR range for display. So in this case yes the values can go above 1
However if you only render to an LDR format in the first place (some games still do this) then values typically won't be above 1.
If you're calculating an average luminance value for the purpose of exposure control, then yes the value can most definitely be higher than 1. You'll want to use a floating-point format like R16_FLOAT or F32_FLOAT.
Bloom from a physical perspective is just the lenses not being perfectly clear. They tend to scatter a small amount of the incoming light while it's traversing through the lense. The tone mapper from a physical standpoint is the retina of your eye or the image sensor of a camera, which receives the light after it travelled through the lenses and converts it into clamped electrical impulses.
Conclusion: You have to tonemap the high dynamic range image that already has bloom and other lens flares applied to it and not the other way round.
Overall, it's still perfectly fine to have a white point, where everything brighter than this white point is just clamped to white.