Tell me what you think?

Well, from what I know, his Hollow powers aren't exclusively dependent on his Fullbring powers, since he was able to use Hollow powers well before he even knew what a Fullbring was. However, that's not really the question. To answer your question, no, logically, the powers should die with Ginjo, as he was the one that stole Ichigo's powers, then he died, meaning that every trace of Ichigo's former ability would have died with him - at least, that's the way I see it. Plus, then Ichigo got his Soul Reaper powers back right after Ginjo stole his Fullbring and then used those Shinigami powers to absolutely devastate Ginjo.