importing Illustrator Brush styles?

I can import a path from Illustrator, but can I import the same path with a brush style?

my goal is to make a rainbow-like multi-colored line draw itself on the screen. It would be great to make this happen using the "trim paths" effect on a Shape Layer.

I can make my rainbow line in Illustrator (one path with a multi-colored brush applied to it).

I could rasterize my line, import it into AE and make it "draw on" using masks or the write-on effect. But it would be so much easier to use the "trim paths" effect on a Shape Layer.

Can it be done?