i dunno, i was guessing "maybe feel something". i know when you over "pull" or strain a tendon you can feel it. if a tendon snapped loose, you would feel it. can go into the "how" but i think it has something to do with nerves sending electrons or some shit to the brain that makes you say ouch.
thanks for the picture, i'm going to go read the link also - but i still think unless there is some way to "curl" that small little innner thigh muscle, those girly machines won't really have too much effect. it would be like doing arm curls without curling your arm... your bicep wouldn't contract, and thus not a good workout. yea you would "feel" it in your bicept but not effective as a curling movement.
You are thinking about the muscle all wrong. It is designed to sweep the leg from out to in. Doing the machines and cable sweeps are like doing dumbell flys to work the pec muscles. Try this, sit in a chair and get a long book and put it length ways between your knees. Relax and put your hand on your inner thigh then squeeze, you can feel the muscles tense up. If you have ever tried to do the splits these are the muscles that hurt like a mug
If you want a real test of how those muscles work try spreading your legs and then squeezing them back together while standing on the ice. The abductor (a) and gracilis (b) control the inward sweept of the leg in while the glutes (c), vastus lateralis (d) and sartorius (e) control the outward sweep.
Sorry for the rough photoshopping
Training them does increase squat just as training stabilizing muscles for the chest helps with bench. It lets the big muscles (glute/ham/quad) focus on going up and down and not so much on stability.