I too have a Schuberth C3, and I've found I can put it on with my glasses in place (or, more often, I add the glasses after I don the helmet). And, yes, the sun visor slides down with no interference with my glasses.
A couple of comments about this hat. I find that the chin baffle seals so well that it gets stuffy inside the helmet very quickly. I ride with the top air vent open, and my windshield all the way up (anything above around 60 mph). Even with the shield down, ventilation is not what I would like on a warm day. As a consequence, I usually ride with the (clear) visor either open to the first detent, or all the way open when my windshield is all the way up. Either position easily solves the stuffiness problem.
Since I wear polarized, prescription sun glasses, the flip up tinted visor makes things too dark. It is, however, fabulous in early morning or late afternoon riding when your direction is into the sun. I bring the visor down an inch or two, just enough to shade the sun while my line of sight is straight out below the tinted visor.
And, after I bought the helmet, I discovered elsewhere on this site a link to a helmet evaluation site (in GB, I think). I was VERY disappointed to discover that Shuberth C3 was not highly rated for impacts. All that money, for a helmet that only tested moderately well. Elsewhere on this site I read that the Schuberth comm system is only average in performance but high in cost compared to other systems. It was good to hear someone here say it performs well. I will probably spring for it this winter primarily because of the neatness of its mating with the helmet.
Next time I buy a helmet, I will plan ahead and visit at least a couple of stores and try on every available hat that meets my criteria. I bought this one because my old one was 12 years old, the Schuberth was significantly reduced (on sale), and it is sound rated (I'm losing my hearing and am very sensitive to ambient noise (even with ear plugs)).