You can edit the width in AI so that it just covers the brush. When you import as a comp you'll have a separate layer that you can convert and use as a track matte to reveal the original brush stroke. If you must use a brush then just duplicate the path you want to reveal with trim paths (I usually the pair on a separate layers) then change the stroke back to basic.
This information is in the User Guide under Preparing Illustrator files for Video. That, and actually animating the path are the only reasons to convert a vector layer to a shape layer. notice the red stroke is not visible: TOPICS Error or problem, How to, Performance 6. I'm assuming you want to use shape layer animators. I've drawn a path and am trying to apply a stroke effect like so: But the effect doesn't seem to be showing in my document, see the screengrab of the path itself. Just open up the AI file, change the stroke to basic (delete the brush) and change the stroke width to 3 points, save, then convert to a shape layer again. It is a single point stroke with a 3 point round brush applied. Brushes can be any shape so this makes perfect sense. If you want to convert a vector path to a stroke and not a filled shape, the path in Illustrator cannot have a brush applied.