You can apply any effect on a layer and it will affect all items in that layer as if they were one item. Doing this requires you to know a non-obvious thing about the layer panel. That is that things are selected with the round ball next to the object name (and if its filled its applying an effect)
Image 1: Select the layer from round ball next to it.
Once you click on the sphere you can apply a effect, change strokes or do pathfinder effects on the layer contents. Because effects are live whatever you do on the layer below it will update.
Image 2: Layer selected.
Its worth noting that blurring is a potentially slow operation. So dont be surprised if the 300 dpi a4 size image takes a while to update. Tip: You can lower raster settings or disable the effect while you work with the data.
Image 3: Layer with blur applied to it.
PS: Please note that there is a huge difference in result form blurring each shape and blurring a layer.