You can create a blur design to start with (pre Illustrator symbol). Select a path and then goto the effects menu and add an effect and then save that to the symbols panel. Use it with the sprayer tool etc. Create a vector preset,
If you have already saved it without any effects etc, you can add it later. You can double click the design and then add the effect in isolation mode. All the instances added to the art board will be updated if you change it.
You can modify them individually if you have added them by dragging them to the art board. You can select and then go to the effects menu and apply a blur etc. None of the other instances will be updated
Gaussian, radial, Smart are the only ones available. You can apply either of them to your object and modify the settings and then use that as a preset. There is also the effect menu and stylize and feather where you can also modify the vector design (and either apply before or after to the instances). As you can have multiple effects applied to a path, you can always re-apply any of those effects again. The end result can be seen and modified via the appearance panel.
You can go to the sprayer tool found in the tools bar and then apply the currently selected design. With that set of designs selected, you can go to the effects menu and apply one of the blurs to that. If you go to the appearance panel you will notice that the current selected set of symbol instances will an effects entry which can be modified by double clicking it or just delete it.
If you apply the design as a selection of sprayed artworks and only want the effect to be applied to some of the instances then you can do this. Create a graphic style for the effect (any effect, it doesn't need to be just one). Select a path and add the effect to that. Go to the graphic style panel and right side menu and define a new style. You can now use the sprayer tool and add the instances. Select that set and then go to the styler tool beneath the sprayer icon and select the required style. You can now apply it to a localized area with the tool so perhaps the left side is modified, the rest can be as before.
Styles, Youtube video on subject