Really dumb question, but would this be possible, with or without practicality? Drill a hole in them, perhaps?
It's possible, unequivocally. The first ones were just this, run by Dieter Runkel.
The specifics of how you would do it depend on the levers you're working with. Generally speaking it's going to involve making a little counterbore for the housing on the lever part and removing some of the internal parts (the cable head cradle area etc) to make room for the cable. Whether it's safe or reasonable to do this is up to you.
Importantly, flatbar brake levers are nearly universally made to clamp to a 22.2mm section of handlebar. Drop bars and aero base bars never have this diameter anywhere on them. The stem clamp area on drop bars can be 25.4, 25.8, 26.0, or 31.8, and the smaller section diameter is always 23.8. Depending on the bar and the rider's preference, you might clamp the aux lever to either the stem clamp area or the tapered down area. You will always need to modify the clamping radius of an aluminum 22.2mm part to do this; if you just squish it on, it will very likely crack sooner or later. Whether or not it has the material to give will be up to you to determine.
It's not feasible.
I'm not saying it couldn't be done with levers means for cable brakes, but it would be really rather hard and/or cost more than just buying interrupter levers.
The in-line lever pushes on the housing, effectively making it longer,
while standard levers pull on the inner cable. The pictures at that article show how in-line levers are different.
To do that they catch a cable end stop, but the end of the cable in your case is in the brifter so there's nothing to get hold of. Thus you'd have to design and fabricate something suitable (it might be possible to clamp the cable, with some considerable force). Bear in mind this is a safety-critical system and not something you want to fail, even if the failure doesn't prevent the main brake lever from working.
Problem Solvers make a device to control one brake with two levers (and a similar device to control two brakes with one lever). That starts getting interesting, but then you get into issues of differing cable pull between drop-bar and flat-bar brake levers, which need to be matched to appropriate brakes. It might be possible with levers for cantilever brakes, looking at the accepted answer there. It might also be possible to provide adequate braking performance for what you're riding even with the wrong pull, but it would take an expensive experiment to find out. When I say expensive, a single Problem Solvers brake doubler costs 4× as much as a pair of inline levers.