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Hi Den,
I am not aware how to add the intersection point while drawing polyline. However, below is the link for sample code to create point where polyline intersect. It is a VBA code You may need to modify the code as per your requirements.
http://help.arcgis.com/en/sdk/10.0/vba_desktop/conceptualhelp/index.html#//00010000002m000000
Hope this will be helpful to start with your requirement.
Regards,
Swapna.
So you have your feature class, say featCls
IFeature feat = featCls.CreateFeature
feat.Shape = point //point is the intersection of the pplyline
feat.Store()
That's it, you just added the point to your feature class.