Oh! Gosh. I forgot I had posted this after it went a while without replies. Here's an update...
I went ahead and tried it as an eyedropper, a few days after posting this. Long story short: zero issues, still using it as an eyedropper, so far so good.
I did quite a lot of research on the potential for corrosion with the metal section. MOST people warn against doing any pen with exposed metal as an eyedropper. Fair enough. Now, Kaweco say the metal section on the student is chromed brass. That should be reasonably tough as far as corrosion resistance goes. And I wouldn't go chucking an iron gall in there (not that I have any iron gall inks anyway).
But let's be honest: I would be pretty surprised to see a modern ink known to be reasonably pen-safe eat through a chunk of chromed brass. Yes, I get that if I drop that section in a bottle of ink and submerge it for years, it'll probably start dissolving. So take everything I am about to say with a big ol' "DISCLAIMER/WARNING!" If you want the safest possible long-term usage of your pen, don't do this. I personally concluded that the risk was probably minimal and went for it anyway.
Still, it IS a good idea to go with a predictably well-behaved pen-safe ink, so naturally I filled it with Waterman Serenity Blue.
I did NOT grease the section threads. The small bit of prior experience I could find said it was unnecessary as far as leaking, and I didn't have any silicon grease around. This is something I WILL add once this batch of ink is used up and I re-ink the pen. "Impatience" is a very stupid reason not to grease it. And, back to the corrosion issue, grease would help improve the corrosion resistance a bit, at least where you apply it on the threads. That said, there's exposed metal other than the threads in this set-up with this pen.
I was nervous about all of this. Worried about leaking, burping, cracking...the lot. I babied the pen for the first week or so, constant checking for any issues, carefully wiping down the section on uncapping each and every time just in case of any stray ink escaping.
However, it has been a few weeks now, and I can report that there have been ZERO issues. The pen continues to write an absolute treat. No leaking, no flow issues - except, predictably, immediately after filling: it did take a few minutes for ink to saturate the feed, but I believe this is normal with eyedroppers. Nothing but a fantastic instrument that now holds a colossal amount of ink. That said, a few weeks is not THAT much time, so consider this a very early report.
I will try to remember this thread and report back over time if I see any issues developing long-term with the exposed metal on the section having any bad interactions with the ink. It's going to take me a little while to use up this barrel (ha!) of ink I've got in there, but I'll be giving the pen a thorough breakdown and cleaning and inspecting the section for any issues at that time. Will keep you all posted. Hopefully this can serve as a guide for future users.
By the way, if anybody is looking for a review of the Student, I posted one recently - my first review! You can find it here.