But if the question is "Do meguca still need to use their nervous systems to control their bodies?" then severed nerves are severed nerves. Whether or not other tissues are still attached doesn't really matter, because they don't transmit information. Whether you just cut the phone lines or knock down the whole wall, the phone doesn't work either way. (If your assumption is that the Incubators have implanted some sort of alternative nervous system that's non-centralized and so widely distributed that any amount of connecting tissue will suffice for it to function, or even wireless, then that's certainly possible, but I don't recall anything we've witnessed that indicates that it's probable.)
A meguca can survive and potentially recover from nearly anything, but that doesn't mean that they can't be disabled for a time by destroying the mechanisms their bodies need to operate. If they couldn't, then most fights would probably only be able to end when a gem was smashed. If that was the case, you'd think Kyouko would have noticed and caught on to the lichbomb sooner.
Actually, I went back and checked out the fight scene in Episode 5, and after the first time Kyouko hits Sayaka (not stabbing her, but throwing her back about twenty feet to ricochet off a wall), before knowing about her healing powers, she says that should have put Sayaka in the hospital for three months. Now, the "three months" might just be braggadocio on Kyouko's part, but she clearly expected that blow to take Sayaka out of the fight for the time being. And Kyouko has quite a bit of experience with meguca combat.
It seems like the healing capabilities of meguca who aren't specialized in it are neither particularly potent nor quick and have a high grief cost. Trying to fix Sabrina's maimed leg would have filled Mami's gem if Sabrina hadn't been cleansing it, and fixing Oriko's neck took quite a while. Weeks of occasional healing haven't been enough to restore Oriko's missing arm yet. It took multiple meguca multiple days to fix Kyousuke's nerve damage. Given the sheer volume of damage and missing tissue Masami suffered, it's quite possible that healing her would have taken a regular meguca more than the five Seeds it cost to have Rin do it, if it were even possible. Masami's description of what she's heard Rin can do...
...seems to imply that most magical girls can't fix that sort of damage. At least not within a timeframe and cost that would be sane without Sabrina or a Clear Seed around.