It works the same way as a suction cup, and like suction cups it doesn't work on rough surfaces, so depends a bit on your frit. If the frit is really sunshade and thus smooth then it may work fine, if it is real frit that has also be used for the sunshade so has a rough raised surface then it will probably not stick.
Once they are on and stuck they generally do stay long term, more durable than suction cups but a long way off a 3M pad stuck direct to the glass.
Many (most?) of them are not reusable, and the sticky pad you stick to them is also not reusable, so there is nothing saved except the effort of getting them off again and cleaning the residue off the glass, so if you want to be sure of permanent fixing, only use the sticky pad and be prepared for a fight to get it off when you eventually need to. If you have a hire car for a short while, use the anti-static sheet, or part of it, much easier to remove, but you are still sacrificing the sheet and sticky pad, so for regular short hires you are better off with a suction cup.
Some anti-static stickers seem to have some sort of glue on them which helps them stick, or maybe just fills any roughness to help them stick, so some will be better over frit than others.