If anything the tubes get stronger from having internal routing done. Although you drill holes in the tube it is normal practice to reinforce that same hole quite a bit. Plus most commonly you add a smaller tube for the cable to run through. As this is fixed in both end it help stiffen that tube a bit as well.
Given the tiny diameter of the routing tube and the fact it's bent, it really won't be adding much to the stiffness of the frame tube. It will help mitigate the weakness created by drilling the hole.
If anything the tubes get stronger from having internal routing done. Although you drill holes in the tube it is normal practice to reinforce that same hole quite a bit. Plus most commonly you add a smaller tube for the cable to run through. As this is fixed in both end it help stiffen that tube a bit as well.