I've been playing with this on my last project. I needed to show each run as the appearance set in the model. We don't have many options here but you might be lucky if you don't need this on a large assembly like I did.
All these options are REALLY slow and need manual update 😞
Brian Ekins has a VB code but it's processing all lines (curves) one at at time and that takes forever. It creates layers with each color but unfortunatelly the layers are called as the RBG code of the color (very hard to identify and edit)
http://modthemachine.typepad.com/my_weblog/2010/10/changing-drawing-curves-to-match-assembly-color.h...
Another solution on the mCAD forum:
http://www.mcadforums.com/forums/viewtopic.php?f=15&t=9547&p=65732&hilit=Drawing+Line+Color
Inventor forum:
http://forums.autodesk.com/t5/inventor-customization/part-colour-be-line-colour-in-idw/td-p/2888796
In my case it didn't work because it is a large assembly.

You can change your selection to part filter select your component (or select it in the browser) and then right click properties to change it's colour.
This is a partial solution because it's hard to select parts and manually update them all the time (as the assembly changes).
What I end up doing was to create copies of Visible layer calling them Run1, Run2, etc. and changed the color of each one as per the assembly (manual unfortunatelly).Then right click on a part (or assembly in my case) in the browser, choose "select as edges" and then in the Annotate tab, Format, Layer, choose the layer you previouslly created. In this case I can just change the layer and all sheets update.

Side Note:
Haven't tested but this seems to affect performance and increase the drawing file size
Adrian S.
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AIP2012-2020 i7 6700k AMD R9 370
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