Unfortunately the items listed under "Photoshop Effects" are applied raster effects and must have a background. They can't be created without the auto-generated background. So, what can one do? Create the effect where the use of white doesn't matter or means "transparent" -- such as on a mask.
Apply the effect to an Opacity Mask rather than the object itself.
- Select the rectangle
Edit > Copy
- Click the
Make Mask button on the Transparency Panel.
This will create a little mask thumbnail on the panel.
- Click the Mask Thumbnail on the Transparency Panel
Edit > Paste in Front This will paste the rectangle in the same position on the mask
- Fill the pasted rectangle with the
Registration color from the Swatch Panel. This is a mask so you want the rectangle to use all the colors. This is about the only time you'd ever use the
Registration swatch for artwork.
- Now apply the
Spatter effect to this rectangle on the mask.
- When applied, you may need to click the
Invert Mask option on the Transparency Panel
- Click the artwork thumbnail on the Transparency Panel to go back to editing artwork.
- To edit the mask again in the future, you must click the mask thumbnail on the Transparency Panel
(Yellow added so transparency can be seen.)
Be aware: This is sill a raster effect. It is merely now on a mask rather on the object itself. You'll want to ensure the
Effect > Document Raster Effects Settings is appropriately set before any output.