In the stories immediately following "Scorpion", it's made fairly clear that Seven would die if the implants were not removed. The implants depended upon constant contact with the collective to continually adapt to the host body and prevent biological rejection of foreign matter. Without that contact, her body was attempting to reject the material, but it was so deeply entwined with her biological systems that the rejection would have killed her.
The Doctor was only able to save her by not just removing the implants but replacing biological systems that had been too tightly entwined (or completely replaced) by implants. Even then, of course, there was still severe psychological trauma at having been removed from the collective, which required constant attention from both the Doctor (who was really not much of a shrink but legally the only one qualified) and Janeway (who more or less adopted Seven as her responsibility, having ordered the plug to be pulled on her connection with the collective).