I'm getting ready to recable my race bike, which currently has Yokozuna installed. It shifts fine, but weighs a ton. I've thought about going to one of the link-based systems to drop some weight (Aican, specifically), but I understand they can get knocked out of "shape". When that happens, does it affect shift/brake performance?

I don't find that it does. When I first set up my TT bike, the rear Nokon loop would actually flop down so that it would loop upwards to the derailleur. I wouldn't notice anything until I looked down. Some zip ties fixed it. Even if they are a bit weird, usually the tension/release keeps things in smooth enough order that you don't notice anything.

I think as long as you keep the links snug against each other, they'll maintain their shape. I'm using Aicans and have them on relatively tight bends -- they seem to be holding up.

i use nokon/powercordz (with powercordz liner), haven't noticed any performance change with cable position, the lack of cable stretch and housing compression made the shifting much snappier than the gore ride-on they replaced

Absolutely no problems with iLink provided they were installed nice and snug.

I had a little trouble making the bend from a DA shifter into a Vukasprint bar. The links separated while snaking cable around and when they came back together it wasn't perfect and the segmented liner got munched and ended up binding the cable. A quick tip is that I now take the length of segmented housing that I will either have under the bar tape, or that passes internally in a bar with internal routing (this is actually fairly important because if you pull the cable nothing is holding the links together and you have a bar full of loose links), drop them on a spare cable with the appropriate end piece compress them and wrap them in a layer of electrical tape. This keeps them compressed in an area that is difficult to work, with especially around curves. It also makes changing cable much much easier.
You can even continue this out to the cable stops and then cut the electrical tape off after the bike is fully cabled.
The other important thing with these and the Alligator is to be really gentle with the liner. It is much easier to get the liner right with the Aican as it is segmented but you still need to watch it carefully. A kink or too hard a pull or squeeze on the Alligator liner and it will never shift right.