While I can't answer about specifics of the drill bit selection/etc, I can tell you that the rough cut (chafed, splintered, etc, per your description) would not be helped by applying CA. Besides, CA is not likely to penetrate deeply into the wood, and the internal drilling would still be through un-treated balsa.
Instead, your work piece needs to be solidly anchored or clamped down, your drilling tool needs to be SHARP, your waste removal should be aggressive (pull the bit out and clean the hole often, especially if the bit itself is not removing wasted effectively), and then you need to start asking your questions about bit types, feed rates, RPM, etc---
I would recommend the CA after the hole is rough cut, to allow you to clean up the drilled hole to a more precise diameter and smooth the walls. You probably don't want to add all the weight of soaking the entire block with CA.
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